System and method for sample processing

ABSTRACT

A method is disclosed that permits calculation of reagent concentrations (in SI units) over time and space within a tissue sample as the sample is immersed in the reagent and the reagent diffuses into the tissue sample. The disclosed method has yielded the surprising result that once a formaldehyde concentration at all points within a tissue sample exceeds about 90 mM during a cold step of a cold+hot fixation protocol, the hot step of the fixation protocol can be commenced to provide reliable detection of molecular targets and preservation of tissue morphology in downstream analyses.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application is a continuation of International ApplicationNo. PCT/US17/67811 filed on Dec. 21, 2017, which application claims thebenefit of the filing date of U.S. Provisional Patent Application No.62/437,962, filed Dec. 22, 2016, and the benefit of the filing date ofU.S. Provisional Patent Application No. 62/438,152, filed Dec. 22, 2016,the disclosures of which are hereby incorporated by reference herein intheir entireties.

FIELD OF THE DISCLOSURE

The present disclosure generally relates to systems and methods forensuring a biological sample is properly preserved for analysis. Moreparticularly, the present disclosure relates to systems and methods forensuring that a cellular sample is sufficiently fixed to provideconsistently good staining of tissue and/or cellular components.

BACKGROUND

Proper preservation of biological samples (such as surgical resections)is of great importance to their subsequent analysis. Currently, thereare no standard procedures for fixing samples and this lack ofstandardization leads to a variety of quality issues in subsequentanalyses. For example, following removal of a tissue sample from asubject, the sample is typically placed into a liquid that will suspendthe metabolic activities of the cells and preserve its morphology. Thisprocess is commonly referred to as “fixation” and can be accomplished byseveral different types of liquids. However, the most common fixativeused to preserve samples for subsequent preparation and analysis is 10%neutral buffered formalin (NBF).

“Fixation” in 10% NBF serves to preserve tissue by cross-linking ofproteins and nucleic acids. The cross-linking preserves thecharacteristics of the tissue, such as the tissue structure, cellstructure and molecular integrity. Typically, fixation with 10% NBFtakes several hours and can be thought of as two separate steps. Firstis the diffusion step of formalin into the tissue. In the second step,formalin molecules interact with biological molecules in the tissue toform cross-links. These cross-links can help keep the cellular structureintact during subsequent processing steps such as tissue dehydration,clearing, embedding in paraffin, sectioning, de-paraffinization, andstaining.

However, if the tissue is “over-fixed,” it may be difficult to diffuseprocessing liquids through the tissue due to an overly extensive networkof cross-linked molecules that limit paths for diffusion. This canresult in inadequate penetration of subsequent processing liquids. Ifthe processing liquid is a stain, slow diffusion rates can cause unevenand inconsistent staining. These types of problems can be increased ifthe “stain” includes relatively large molecules. For example, conjugatedbiomolecules (such as antibody or nucleic acid probe molecules) can berelatively large, often having a mass of several hundred kilodaltons,causing them to diffuse slowly into solid tissue, particularly if thetissue is over-fixed. While over-fixation can sometimes be remedied byextensive antigen and target retrieval procedures, such procedures aretime consuming and not always successful, particularly for retrieval oflabile biomarkers such as phosphorylated proteins.

If the tissue is under-fixed, the tissue may be degraded, for example,by autocatalytic destruction, leading to loss of tissue and cellularmorphology as well as loss of protein and nucleic acid markers ofdiagnostic significance. Furthermore, processing after incompletefixation of a sample can also lead to loss of morphological features ofdiagnostic significance. For example, without a sufficient network ofcross-linked molecules, cells, nuclei and cytoplasm can shrink duringdehydration steps. Accordingly, under-fixed tissue may be unsuitable forexamination and is often discarded.

Conventional pathology practice is often based on predetermined fixationsettings based on empirical knowledge of processing times for sampledimensions (e.g., thicknesses) and tissue type. It is often difficult toproperly stain tissue without knowing this information; tissue is thusoften tested to obtain such information. Unfortunately, the testing maybe time-consuming, destroy significant portions of sample, and lead toreagent waste. By way of example, numerous iterations with differentantigen retrieval settings for IHC/ISH stains may be performed in orderto match and/or compensate for an unknown fixation state and an unknowntissue composition. The repeated staining runs result in additionalsample material consumption and lengthy periods for diagnosis.

BRIEF SUMMARY OF THE DISCLOSURE

Disclosed are a system and method for determining the concentration of areagent (such as formaldehyde) at a particular spatial point(s) atparticular time(s) within a biological sample, rather than as an averageacross the entire sample cross-section. The system and method are basedon acoustic time-of-flight (TOF) information correlated with a diffusionmodel to reconstruct the concentration of the reagent (such asformaldehyde) at a particular point(s) within a tissue sample over timeas the reagent diffuses into the sample.

In one aspect of the present disclosure is a method is provided fordetermining a reagent concentration at a particular point(s) within asample immersed within a reagent, at a given time, the method includingsimulating a spatial dependence of diffusion into the sample over aplurality of time points and for each of a plurality of candidatediffusivity constants to generate a model time-of-flight, and comparingthe model time-of-flight with an experimental time-of-flight to obtainan error function, wherein a minimum of the error function yields thediffusivity constant for the sample. The method further includesproviding a plurality of candidate tissue porosities and using each ofthese candidate tissue porosities to generate a model time-of-flightusing the diffusivity constant and comparing the model time-of-flightwith an experimental time-of-flight to obtain a second error function,wherein a minimum of the error function yields the porosity of thesample. From the determined diffusivity constant and the porosity of thesample, the concentration at a particular point or points within thesample at a particular time can be calculated.

The method has yielded the surprising result that once a formaldehydeconcentration of above about 100 mM (such as above 90 mM) is reached ina tissue sample, quality detection (“staining”) of molecular targets andfaithful morphological integrity, as judged by pathologist scoringagainst industry “gold standards,” is reliably achieved, yielding abetter receiver operating characteristic (ROC) curve of relative truepositives versus false positives than previous results for modeleddiffusivity constants alone. Furthermore, the addition of spatialinformation regarding true reagent concentration and an understandableSI unit of measure makes it possible to utilize other techniques, suchas radio-label tracing, mid-IR or magnetic resonance techniques todirectly determine when this threshold formaldehyde concentration isreached within a particular type, size and shaped sample, eitherstatically or dynamically (e.g. in real-time), in order to help ensurethat quality staining will be obtained at any given point(s) in a tissuesample. In other words, using the disclosed method it is possible toarrive at a fixation level for a tissue sample (or portion thereof, suchas at the center) that is sufficient to preserve morphology andbiomarkers within the sample without unduly complicating furtheranalysis through over-fixation.

In an alternative embodiment, once a concentration sufficient topreserve one biomarker for reliable detection is achieved in aparticular spatial portion of the sample, other portions of the samplecan be selected to have higher or lower concentrations of formalin thatare better suited for detection of one or more additional biomarkers. Inyet another alternative embodiment, based on a known formaldehydeconcentration distribution reached during fixation of a particularsample type of a particular shape for a particular time, selectedportions (such as selected tissue sections) of the sample can beutilized for different tests according to the optimal formaldehydeconcentration for the particular test (such as a test for a labilemarker such as FoxP3 or RNA). The fixation can be carried out either atroom temperature or using a cold+hot protocol as described herein. Moreparticularly, in a cold+hot protocol, the optimal formaldehydeconcentration is reached during the cold step.

In another aspect of the present disclosure is a system including anacoustic monitoring device that detects acoustic waves that havetraveled through a tissue sample, and a computing device communicativelycoupled to the acoustic monitoring device, the computing device isconfigured to evaluate a speed of the acoustic waves based on atime-of-flight and including instructions, when executed, for causingthe processing system to perform operations comprising setting a rangeof candidate diffusivity constants for the tissue sample, simulating aspatial dependence of a reagent within the tissue sample for a pluralityof time points and for a first of the range of candidate diffusivitypoints, determining a modeled time-of-flight based on the spatialdependence, repeating the spatial dependence simulation for each of theplurality of diffusivity constants, and determining an error between themodeled-time-of-flight for the plurality of diffusivity constants versusan experimental time-of-flight for the tissue sample, wherein a minimumof an error function based on the error yields a diffusivity constantfor the tissue sample. The system further includes instructions, whenexecuted, for causing the processing system to perform operationscomprising setting a range of candidate porosities for the tissue samplethat includes a plurality of candidate porosities (such as between about0.05 and about 0.50, for example between about 0.05 and about 0.40 orbetween about 0.05 and about 0.30), determining a second modeledtime-of-flight based on the diffusivity constant of the sample and afirst of the plurality of candidate porosities, and determining a seconderror between the experimental time-of-flight and the second modeledtime-of-flight, repeating the determination of the second modeledtime-of-flight for others of the plurality of candidate porosities and acorresponding second error, wherein a minimum of the error identifiesthe porosity of the sample. In more particular embodiments, the systemfurther includes instructions, that when executed, yield a spatialconcentration distribution of the reagent within the sample at aparticular time. In an even more particular embodiment, the systemfurther includes instructions, that when executed provide a reagentconcentration at the center of the sample at a particular time. In stillan even more particular embodiment, such a reagent concentration can beutilized to terminate infusion of the sample with the reagent when apre-determined concentration is reached at a particular point or regionwithin the sample, such as at the center of the sample.

In yet another aspect of the present disclosure is a tangiblenon-transitory computer-readable medium is provided to storecomputer-readable code that is executed by a processor to performoperations including comparing a simulated time-of-flight for a samplematerial with an experimental time-of-flight for the sample material,obtaining a diffusivity constant for the sample material based on aminimum of an error function between the simulated time-of-flight andthe acoustic time-of-flight, comparing a second simulated time-of-flightfor a sample material obtained using the diffusivity constant and theexperimental decay constant (tau) to the experimental time-of-flight,obtaining a porosity for the sample material based on a minimum of asecond error function, and optionally calculating a spatial distributionof the concentration of the reagent or a concentration of the reagent ata particular point or region of the sample.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a tissue processing system 100 for optimized tissuefixation, according to an exemplary embodiment of the subjectdisclosure.

FIGS. 2A and 2B respectively show depictions of ultrasound scan patternsfrom a biopsy capsule and from a standard-sized cassette.

FIG. 2C shows a timing diagram for an exemplary embodiment of thesubject disclosure.

FIG. 3 shows a method for obtaining a diffusivity coefficient for atissue sample.

FIG. 4 shows an alternate method for obtaining a diffusivity coefficientfor a tissue sample.

FIG. 5A shows a simulated concentration gradient for a first time point,and for several time points over the course of an experiment.

FIG. 5B shows a simulated concentration gradient for a first time point,and for several time points over the course of an experiment.

FIGS. 6A and 6B respectively depict plots of the simulated amount ofdetected concentration of NBF by the ultrasound over the course of theexperiment (FIG. 6A) and the simulated (FIG. 6B) TOF signal for thefirst candidate diffusivity constant.

FIG. 7 depicts temporally varying TOF signals calculated for allpotential diffusivity.

FIG. 8A depicts experimentally calculated TOF trends collected from a 6mm piece of human tonsil sample.

FIG. 8B depicts a spatially-averaged TOF signal collected from a 6 mmpiece of human tonsil sample.

FIGS. 9A and 9B respectively show plots of the calculated error functionbetween simulated (FIG. 9A) and experimentally measured (FIG. 9B) TOFsignals as a function of candidate diffusivity constant and a zoomed-inview of the error function.

FIG. 10 depicts a TOF trend calculated with a modeled diffusivityconstant plotted alongside an experimental TOF.

FIGS. 11A and 11B each show reconstructed diffusivity constants for themultiple tissue samples.

FIG. 12A depicts a system comprising a transmitter and a receiver pairfor measuring TOF via phase shifts.

FIG. 12B depicts a system comprising a transmitter and a receiver pairfor measuring TOF via phase shifts.

FIG. 13 shows a model of diffusion of a reagent into a cylindricalobject, such as a cylindrical tissue core.

FIG. 14 shows a typical distribution of the percent diffusion of areagent into the tissue sample center at 3 hours and 5 hours.

FIG. 15 shows a typical ROC curve of staining quality (based onsensitivity and specificity) based on percent diffusion at the tissuesample center.

FIG. 16 shows a typical graph of the differential in percent diffusionat the tissue sample center between about 3 hours and about 5 hours ofexposure to a reagent.

FIG. 17 shows the raw data distribution of tonsil tissue volume porositydetermined according to a disclosed embodiment.

FIG. 18 shows a box and whisker distribution of tonsil tissue volumeporosity determined according to a disclosed embodiment.

FIG. 19 shows a typical distribution of formaldehyde concentration atthe tissue sample center as determined according to a disclosedembodiment at 3 hours and 5 hours.

FIG. 20 shows a typical ROC curve of staining quality (based onsensitivity and specificity) based on formaldehyde concentration at thetissue sample center.

FIG. 21 shows a typical graph of the differential in formaldehydeconcentration at the tissue sample center between 3 hours and 5 hours ofimmersion in an NBF solution.

FIG. 22 shows the distributions of raw porosities for several tissuetypes as determined according to a disclosed embodiment.

FIG. 23 shows a set of box and whisker distributions of porosities forseveral tissue types as determined according to a disclosed embodiment.

FIG. 24 shows the distributions of diffusivity constants for severaltissue types.

FIG. 25 shows a set of box and whisker distributions of diffusivityconstants for several tissue types.

FIG. 26 shows the distributions of raw percent diffusion at the tissuesample center at 3, 5 and 6 hours for several tissue types.

FIG. 27 shows a set of box and whisker distributions of percentdiffusion at the tissue sample center at 3, 5 and 6 hours for severaltissue types.

FIG. 28 shows the distributions of raw formaldehyde concentrations atthe tissue sample center at 3, 5 and 6 hours for several tissue types.

FIG. 29 shows a set of box and whisker distributions of formaldehydeconcentration at the tissue sample center at 3, 5 and 6 hours forseveral tissue types.

FIG. 30 shows distributions of raw formaldehyde concentrations at thetissue sample center for several tissue types after the indicatedimmersion times.

FIG. 31 shows a set of box and whisker distributions of formaldehydeconcentration at the tissue sample center for several tissue types afterthe indicated immersion times.

FIG. 32 shows a labeled version of FIG. 31, dividing tissue types thatprovide optimal staining after either 5 or 6 hours of immersion in about10% NBF.

FIG. 33 shows the raw distribution of formaldehyde concentration at thetissue sample center for all tissues after 6 hours of immersion in about10% NBF.

FIG. 34 show the box and whisker distribution of formaldehydeconcentration at the tissue sample center for all tissues after 6 hoursof immersion in about 10% NBF.

FIG. 35 shows a method for obtaining a diffusivity coefficient, aporosity, and formaldehyde concentration at the tissue sample center.

DETAILED DESCRIPTION

It should also be understood that, unless clearly indicated to thecontrary, in any methods claimed herein that include more than one stepor act, the order of the steps or acts of the method is not necessarilylimited to the order in which the steps or acts of the method arerecited.

As used herein, the singular terms “a,” “an,” and “the” include pluralreferents unless context clearly indicates otherwise. Similarly, theword “or” is intended to include “and” unless the context clearlyindicates otherwise. The term “includes” is defined inclusively, suchthat “includes A or B” means including A, B, or A and B.

As used herein in the specification and in the claims, “or” should beunderstood to have the same meaning as “and/or” as defined above. Forexample, when separating items in a list, “or” or “and/or” shall beinterpreted as being inclusive, i.e., the inclusion of at least one, butalso including more than one, of a number or list of elements, and,optionally, additional unlisted items. Only terms clearly indicated tothe contrary, such as “only one of” or “exactly one of,” or, when usedin the claims, “consisting of,” will refer to the inclusion of exactlyone element of a number or list of elements. In general, the term “or”as used herein shall only be interpreted as indicating exclusivealternatives (i.e. “one or the other but not both”) when preceded byterms of exclusivity, such as “either,” “one of,” “only one of” or“exactly one of.” “Consisting essentially of,” when used in the claims,shall have its ordinary meaning as used in the field of patent law.

The terms “comprising,” “including,” “having,” and the like are usedinterchangeably and have the same meaning. Similarly, “comprises,”“includes,” “has,” and the like are used interchangeably and have thesame meaning. Specifically, each of the terms is defined consistent withthe common United States patent law definition of “comprising” and istherefore interpreted to be an open term meaning “at least thefollowing,” and is also interpreted not to exclude additional features,limitations, aspects, etc. Thus, for example, “a device havingcomponents a, b, and c” means that the device includes at leastcomponents a, b and c. Similarly, the phrase: “a method involving stepsa, b, and c” means that the method includes at least steps a, b, and c.Moreover, while the steps and processes may be outlined herein in aparticular order, the skilled artisan will recognize that the orderingsteps and processes may vary.

As used herein in the specification and in the claims, the phrase “atleast one,” in reference to a list of one or more elements, should beunderstood to mean at least one element selected from any one or more ofthe elements in the list of elements, but not necessarily including atleast one of each and every element specifically listed within the listof elements and not excluding any combinations of elements in the listof elements. This definition also allows that elements may optionally bepresent other than the elements specifically identified within the listof elements to which the phrase “at least one” refers, whether relatedor unrelated to those elements specifically identified. Thus, as anon-limiting example, “at least one of A and B” (or, equivalently, “atleast one of A or B,” or, equivalently “at least one of A and/or B”) canrefer, in one embodiment, to at least one, optionally including morethan one, A, with no B present (and optionally including elements otherthan B); in another embodiment, to at least one, optionally includingmore than one, B, with no A present (and optionally including elementsother than A); in yet another embodiment, to at least one, optionallyincluding more than one, A, and at least one, optionally including morethan one, B (and optionally including other elements); etc.

I. TECHNICAL IMPLEMENTATION

The present disclosure provides systems and computer-implemented methodsfor calculating the diffusivity constant (also known as “diffusioncoefficient”) and/or a porosity of a sample (e.g. through the use ofacoustic time-of-flight (TOF) based information correlated with adiffusion model to reconstruct a spatiotemporal concentration profileacross a tissue sample).

In some embodiments, tissue preparation systems and methods disclosedherein may be adapted to monitor the diffusion of fixative fluid into atissue sample until a pre-determined concentration level is reached. Forexample, as formalin penetrates into tissue, it displaces interstitialfluid. This fluid exchange at least partially changes the composition ofthe tissue volume, and this change may be monitored. By way of example,given that interstitial fluid and formalin each react differently to anintroduced ultrasound pulse (i.e. each fluid has a discrete “soundvelocity” property), an output ultrasound pulse will accumulate a smalltransit time differential that increases as more fluid exchange occurs,i.e. as more formalin displaces interstitial fluid. This enablesoperations such as determining the phase differential accumulated bydiffusion based on the geometry of the tissue sample, modeling theimpact of the diffusion on the TOF, and/or using a post-processingalgorithm to correlate the results to determine the diffusivityconstant. Moreover, the sensitivity of the disclosed TOF instruments candetect a change of less than 10 parts per million enabling potentiallymore accurate characterization of the diffusivity constant and porosity.On the nanosecond TOF scale, all fluids and tissues will have discretesound velocities, so the disclosed operations are not limited to solelyquantifying water diffusion but may be used to monitor the diffusion ofall fluids into all tissues. For example, diffusion of dehydratingreagents (such as graded ethanols), clearing agents (such as xylene) andparaffin used for embedding of a tissue sample.

The rate of diffusion may be monitored by a system of acoustic probesbased on the different acoustic properties of formalin-soaked tissuesamples. Such a system for diffusion monitoring and experimental TOFmeasurement is described in further detail U.S. Patent Publication Nos.2013/0224791, 2017/0284969, 2017/0336363, 2017/0284920, and 2017/0284859the disclosures of which are each incorporated by reference herein intheir entireties. Another suitable system for diffusion monitoring andexperimental TOF measurement is also described in the internationalpatent application entitled ACCURATELY CALCULATING ACOUSTICTIME-OF-FLIGHT filed in Dec. 17, 2015, the contents of each of which arehereby incorporated by reference herein in their entirety.

Further examples of suitable systems and methods for TOF monitoring aredescribed in PCT Publication No. WO2016/097163 and US Patent PublicationNo. 2017/0284859, the contents of which are also incorporated byreference herein to the extent they are not inconsistent with thepresent disclosure. The referenced applications describe solid tissuesamples being contacted with a liquid fixative that travels through thetissue samples and diffuses throughout substantially the entirethickness of the tissue samples and being analyzed based on acousticcharacteristics that are continuously or periodically monitored toevaluate the state and condition of the tissue sample throughoutprocessing. For example, a fixative such as formalin having a bulkmodulus greater than interstitial fluid can significantly alter the TOFas it displaces the interstitial fluid. Based on the obtainedinformation, a fixation protocol may be adjusted to enhance processingconsistency, reduce processing times, improve processing quality, or thelike. The acoustic measurements may be used to non-invasively analyzetissue samples. The acoustic properties of tissue samples may change asliquid reagent (e.g., a liquid fixative) travels through the sample. Thesample's acoustic properties can change during, for example, a pre-soakprocess (e.g., diffusion of cold fixative), a fixation process, astaining process, or the like. In the fixation process (e.g., across-linking process), the speed of transmission of acoustic energy canchange as the tissue sample becomes more heavily cross-linked. Real-timemonitoring can be used to accurately track movement of the fixativethrough the sample. For example, a diffusion or fixation status of abiological sample can be monitored based on a time-of-flight (TOF) ofacoustic waves. Other examples of measurements include acoustic signalamplitude, attenuation, scatter, absorption, phase shifts of acousticwaves, or combinations thereof.

In some embodiments, the movement of the fixative through the tissuesample may be monitored in real-time.

II. SYSTEMS AND METHODS

A “time-of-flight” or “TOF” as used herein is, for example, the timethat it takes for an object, particle or acoustic, electromagnetic orother wave to travel a distance through a medium. The TOF may bemeasured empirically e.g. by determining a phase differential betweenthe phases of an acoustic signal emitted by a transmitter (“transmittedsignal”) and an acoustic signal received by a receiver (“receivedsignal”) that has passed through an object immersed in a fluid and anacoustic signal that has passed through the fluid alone.

As used herein, the term “biological sample,” “biological specimen,”“tissue sample,” “sample,” or the like refers to any sample including abiomolecule (such as a protein, a peptide, a nucleic acid, a lipid, acarbohydrate, or a combination thereof) that is obtained from anyorganism including viruses. Other examples of organisms include mammals(such as humans; veterinary animals like cats, dogs, horses, cattle, andswine; and laboratory animals like mice, rats and primates), insects,annelids, arachnids, marsupials, reptiles, amphibians, bacteria, andfungi. Biological samples include tissue samples (such as tissuesections and needle biopsies of tissue), cell samples (such ascytological smears such as Pap smears or blood smears or samples ofcells obtained by microdissection), or cell fractions, fragments ororganelles (such as obtained by lysing cells and separating theircomponents by centrifugation or otherwise). Other examples of biologicalsamples include blood, serum, urine, semen, fecal matter, cerebrospinalfluid, interstitial fluid, mucous, tears, sweat, pus, biopsied tissue(for example, obtained by a surgical biopsy or a needle biopsy), nippleaspirates, cerumen, milk, vaginal fluid, saliva, swabs (such as buccalswabs), or any material containing biomolecules that is derived from afirst biological sample. In certain embodiments, the term “biologicalsample” as used herein refers to a sample (such as a homogenized orliquefied sample) prepared from a tumor or a portion thereof obtainedfrom a subject. The samples may be contained e.g. on a tissue sampleslide.

The “Porosity” is a measure of the void (i.e. “empty”) spaces in amaterial and is a fraction of the volume of voids over the total volumeof an object, between 0 and 1, or as a percentage between 0 and 100%. A“porous material” as used herein refers to, for example, a 3D objecthaving a porosity larger than 0.

A “diffusion coefficient” or “diffusivity constant” as used herein is,for example, a proportionality constant between the molar flux due tomolecular diffusion and the gradient in the concentration of the objectwhose diffusion is observed (or the driving force for diffusion).Diffusivity is encountered e.g. in Fick's law and numerous otherequations of physical chemistry. The higher the diffusivity (of onesubstance with respect to another), the faster they diffuse into eachother. Typically, a compound's diffusivity constant is ˜10,000× as greatin air as in water. Carbon dioxide in air has a diffusivity constant of16 mm2/s, and in water its diffusivity constant is 0.0016 mm2/s.

A “phase differential” as used herein is, for example, the difference,expressed in degrees or time, between two waves having the samefrequency and referenced to the same point in time.

A “biopsy capsule” as used herein is, for example, a container for abiopsy tissue sample. Typically, a biopsy capsule comprises a mesh forholding the sample and letting a liquid reagent, e.g. a buffer, afixation solution or a staining solution surround and diffuse into atissue sample. A biopsy capsule can maintain the sample in a particularshape, which shape can advantageously provide the sample with a shapethat is computationally easier to model according to the disclosedmethod and thus be more suitable for use in a disclosed system. A“cassette” as used herein refers to, for example, a container for abiopsy capsule or a tissue sample not contained within a biopsy capsule.Preferentially, the cassette is designed and shaped such that it canautomatically be selected and moved, e.g. raised and lowered, relativeto the beam path of an ultrasonic transmitter-receiver pair, and furtherhas openings that permit movement of a liquid reagent into and out ofthe cassette and thus further into and out of a tissue sample heldwithin. The movement may be performed for example by a robotic arm oranother automated movable component of a device onto which the cassetteis loaded. In other embodiments, a cassette alone is use for containinga tissue sample and the shape of the cassette can, at least in part,determine the shape of the tissue sample. For example, placing arectangular tissue block that is slightly thicker that the depth of acassette into a cassette and closing the cassette lid can cause thetissue sample to be compressed and spread to fill a greater portion ofthe inner space of the cassette, and thus be transformed into a thinnerpiece having a greater height and width, but having a thicknesscorresponding roughly to the depth of the cassette.

In some embodiments, a system of calculating a formaldehydeconcentration or other reagent is provided, the system including asignal analyzer having a processor and a memory coupled to theprocessor, the memory to store computer-executable instructions that,when executed by the processor, cause the processor to performoperations including calculation of a formalin concentration from a setof acoustic data as discussed in further detail below.

In some embodiments, a data input into the signal analyzer is anacoustic data set generated by an acoustic monitoring system, where theacoustic data set is generated by transmitting an acoustic signal sothat the acoustic signal encounters a material of interest, and thendetecting the acoustic signal after the acoustic signal has encounteredthe material of interest. In some embodiments, a system is providedcomprising a signal analyzer as disclosed herein and an acousticmonitoring system discussed in further detail below. Additionally, oralternatively, a system may be provided comprising a signal analyzer asdisclosed herein and a non-transitory computer readable mediumcomprising an acoustic data set obtained from an acoustic monitoringsystem as disclosed herein. In an embodiment, the acoustic data isgenerated by frequency sweep transmitted and received by the acousticmonitoring system. As used herein, the term “frequency sweep” shallrefer to a series of acoustic waves transmitted at fixed intervals offrequencies through a medium, such that a first set of acoustic waves isemitted through the medium at a fixed frequency for a first fixedduration of time, and subsequent sets of acoustic waves are emitted atfixed frequency intervals for subsequent—preferably equal—durations.

In some embodiments, the system is adapted for monitoring diffusion of afluid into a porous material. In such an embodiment, a system may beprovided comprising: (a) a signal analyzer; (b) an acoustic monitoringsystem as discussed herein and/or a non-transitory computer readablemedium comprising an acoustic data set generated by said acousticmonitoring system; and (c) an apparatus for holding a porous materialimmersed in a volume of a fluid. In some embodiments, the system isadapted to monitor diffusion of a fixative into a tissue sample.

In some embodiments, the formalin concentration or other reagentconcentration is determined for the purpose of characterizing the extentto which a reagent has penetrated a porous object. For example, themethod may be used for monitoring a staining process of an object, e.g.cloth, plastics, ceramics, tissues or others, for monitoring a fixationprocess or other tissue processing step, such as dehydration, clearingand paraffin embedding.

In some embodiments, the present disclosure provides an acousticmonitoring system for collecting an acoustic data set, the acousticmonitoring system comprising a transmitter and a receiver, wherein thetransmitter and receiver are arranged such that acoustic signalsgenerated by the transmitter are received by the receiver andtransformed into a computer-readable signal. In some embodiments, thesystem comprises an ultrasonic transmitter and an ultrasonic receiver.As used herein, a “transmitter” refers to a device capable of convertingan electrical signal to acoustic energy. As used herein, an “ultrasonictransmitter” refers a device capable of converting an electrical signalto ultrasonic acoustic energy. As used herein, a “receiver” is a devicecapable of converting an acoustic wave to an electrical signal; and an“ultrasonic receiver” is a device capable of converting ultrasonicacoustic energy to an electrical signal.”

In some embodiments, certain materials useful for generating acousticenergy from electrical signals are also useful for generating electricalsignals from acoustic energy. In some embodiments, the transmitter andreceiver do not necessarily need to be separate components, althoughthey can be. In some embodiments, the transmitter and receiver arearranged such that the receiver detects acoustic waves generated by thetransmitter after the transmitted waves have encountered a material ofinterest. In some embodiments, the receiver is arranged to detectacoustic waves that have been reflected by the material of interest. Inother embodiments, the receiver is arranged to detect acoustic wavesthat have been transmitted through the material of interest.

In some embodiments, the transmitter comprises at least a waveformgenerator operably linked to a transducer, the waveform generator beingconfigured to generate an electrical signal that is communicated to thetransducer, the transducer being configured for converting theelectrical signal to an acoustic signal. In some embodiments, thewaveform generator is programmable, such that a user may modify certainparameters of the frequency sweep, including for example: startingand/or ending frequency, the step size between frequencies of thefrequency sweep, the number of frequency steps, and/or the duration forwhich each frequency is transmitted. In other embodiments, the waveformgenerator is pre-programmed to generate one or more a pre-determinedfrequency sweep pattern. In other embodiments, the waveform generatormay be configured to transmit both pre-programmed frequency sweeps andcustomized frequency sweeps. The transmitter may also contain a focusingelement, which allows the acoustic energy generated by the transducer tobe predictably focused and directed to a specific area of an object.

In some embodiments, the transmitter can transmit a frequency sweepthrough the medium, which is then detected by the receiver andtransformed into the acoustic data set to be stored in a non-transitorycomputer readable storage medium and/or transmitted to the signalanalyzer for analysis. In some embodiments, where the acoustic data setincludes data representative of a phase difference between thetransmitted acoustic waves and the received acoustic waves, the acousticmonitoring system may also include a phase comparator. In someembodiments, the phase comparator generates an electrical signal thatcorresponds to the phase difference between transmitted and receivedacoustic waves. In some embodiments, the acoustic monitoring systemcomprises a phase comparator communicatively linked to a transmitterand/or a receiver. In some embodiments, where the output of the phasecomparator is an analog signal, the acoustic monitoring system may alsoinclude an analog to digital converter for converting the analog outputof the phase comparator to a digital signal. In some embodiments, thedigital signal may then be recorded, for example, on a non-transitorycomputer readable medium, or may be communicated directly to the signalanalyzer for analysis. Alternatively, and in some embodiments, thetransmitter can transmit acoustic energy at a particular frequency andthe signal detected by the receiver is stored and analyzed for its peakintensity.

In some embodiments, a signal analyzer is provided containing aprocessor and a memory coupled to the processor, the memory to storecomputer-executable instructions that, when executed by the processor,cause the processor to calculate a formalin concentration based at leastin part on an acoustic data set generated by an acoustic monitoringsystem as discussed above.

The term “processor” encompasses all kinds of apparatus, devices, andmachines for processing data, including by way of example a programmablemicroprocessor, a computer, a system on a chip, or multiple ones, orcombinations, of the foregoing. The apparatus can include specialpurpose logic circuitry, e.g., an FPGA (field programmable gate array)or an ASIC (application-specific integrated circuit). The apparatus alsocan include, in addition to hardware, code that creates an executionenvironment for the computer program in question, e.g., code thatconstitutes processor firmware, a protocol stack, a database managementsystem, an operating system, a cross-platform runtime environment, avirtual machine, or a combination of one or more of them. The apparatusand execution environment can realize various different computing modelinfrastructures, such as web services, distributed computing and gridcomputing infrastructures.

A computer program (also known as a program, software, softwareapplication, script, or code) can be written in any form of programminglanguage, including compiled or interpreted languages, declarative orprocedural languages, and it can be deployed in any form, including as astand-alone program or as a module, component, subroutine, object, orother unit suitable for use in a computing environment. A computerprogram may, but need not, correspond to a file in a file system. Aprogram can be stored in a portion of a file that holds other programsor data (e.g., one or more scripts stored in a markup languagedocument), in a single file dedicated to the program in question, or inmultiple coordinated files (e.g., files that store one or more modules,subprograms, or portions of code). A computer program can be deployed tobe executed on one computer or on multiple computers that are located atone site or distributed across multiple sites and interconnected by acommunication network.

The processes and logic flows described in this specification can beperformed by one or more programmable processors executing one or morecomputer programs to perform actions by operating on input data andgenerating output. The processes and logic flows can also be performedby, and apparatus can also be implemented as, special purpose logiccircuitry, e.g., an FPGA (field programmable gate array) or an ASIC(application-specific integrated circuit).

Processors suitable for the execution of a computer program include, byway of example, both general and special purpose microprocessors, andany one or more processors of any kind of digital computer. Generally, aprocessor will receive instructions and data from a read-only memory ora random access memory or both. The essential elements of a computer area processor for performing actions in accordance with instructions andone or more memory devices for storing instructions and data. Generally,a computer will also include, or be operatively coupled to receive datafrom or transfer data to, or both, one or more mass storage devices forstoring data, e.g., magnetic, magneto-optical disks, or optical disks.However, a computer need not have such devices. Moreover, a computer canbe embedded in another device, e.g., a mobile telephone, a personaldigital assistant (PDA), a mobile audio or video player, a game console,a Global Positioning System (GPS) receiver, or a portable storage device(e.g., a universal serial bus (USB) flash drive), to name just a few.Devices suitable for storing computer program instructions and datainclude all forms of non-volatile memory, media and memory devices,including by way of example semiconductor memory devices, e.g., EPROM,EEPROM, and flash memory devices; magnetic disks, e.g., internal harddisks or removable disks; magneto-optical disks; and CD-ROM and DVD-ROMdisks. The processor and the memory can be supplemented by, orincorporated in, special purpose logic circuitry.

To provide for interaction with a user, embodiments of the subjectmatter described in this specification can be implemented on a computerhaving a display device, e.g., an LCD (liquid crystal display), LED(light emitting diode) display, or OLED (organic light emitting diode)display, for displaying information to the user and a keyboard and apointing device, e.g., a mouse or a trackball, by which the user canprovide input to the computer. In some implementations, a touch screencan be used to display information and receive input from a user. Otherkinds of devices can be used to provide for interaction with a user aswell; for example, feedback provided to the user can be in any form ofsensory feedback, e.g., visual feedback, auditory feedback, or tactilefeedback; and input from the user can be received in any form, includingacoustic, speech, or tactile input. In addition, a computer can interactwith a user by sending documents to and receiving documents from adevice that is used by the user; for example, by sending web pages to aweb browser on a user's client device in response to requests receivedfrom the web browser.

Embodiments of the subject matter described in this specification can beimplemented in a computing system that includes a back-end component,e.g., as a data server, or that includes a middleware component, e.g.,an application server, or that includes a front-end component, e.g., aclient computer having a graphical user interface or a Web browserthrough which a user can interact with an implementation of the subjectmatter described in this specification, or any combination of one ormore such back-end, middleware, or front-end components. The componentsof the system can be interconnected by any form or medium of digitaldata communication, e.g., a communication network. Examples ofcommunication networks include a local area network (“LAN”) and a widearea network (“WAN”), an inter-network (e.g., the Internet), andpeer-to-peer networks (e.g., ad hoc peer-to-peer networks).

The computing system can include any number of clients and servers. Aclient and server are generally remote from each other and typicallyinteract through a communication network. The relationship of client andserver arises by virtue of computer programs running on the respectivecomputers and having a client-server relationship to each other. In someembodiments, a server transmits data (e.g., an HTML page) to a clientdevice (e.g., for purposes of displaying data to and receiving userinput from a user interacting with the client device). Data generated atthe client device (e.g., a result of the user interaction) can bereceived from the client device at the server.

In some embodiments, the signal analyzer accepts as an input an acousticdata set recorded from a test material. The acoustic data set isrepresentative of at least a portion of a frequency sweep that isdetected after the frequency sweep encounters a material of interest. Insome embodiments, the portion of the frequency sweep that is detectedconstitutes acoustic waves that are reflected by the material ofinterest. In other embodiments, the portion of the frequency sweep thatis detected constitutes acoustic waves that have passed through thematerial of interest. Alternatively, the acoustic data set isrepresentative of burst of acoustic energy of a single frequency that isreflected or has passed through the material of interest.

FIG. 1 shows an embodiment of a system useful for tissue processing 100(e.g., for optimized tissue fixation, dehydration, clearing orembedding), according to an exemplary embodiment of the subjectdisclosure. System 100 comprises an acoustic monitoring device 102communicatively coupled to a memory 110 for storing a plurality ofprocessing modules or logical instructions that are executed byprocessor 105 coupled to computer 101. Acoustic monitoring device 102may comprise the aforementioned acoustic probes including one or moretransmitters and one or more receivers. The tissue sample may beimmersed in a liquid fixative while the transmitters and receiverscommunicate to detect time-of-flight (TOF) of acoustic waves.

In some embodiments, the system 100 employs one or more processors 105and at least one memory 110, the at least one memory 110 storingnon-transitory computer-readable instructions for execution by the oneor more processors to cause the one or more processors to executeinstructions (or stored data) in one or more modules, including: atissue analysis module 111 for receiving information about the tissueblock via user input or electronic input and for determining tissuecharacteristics such as an acoustic velocity of the tissue; a TOFmodeling module 112 for simulating a spatial dependence of relativefixative or reagent concentrations for various times and model diffusionconstants to generate a time-varying (“expected” or “modeled”) TOFsignal and outputting a model decay constant; a TOF measurement module113 for determining an actual TOF signal of the tissue, computing aspatial average, and generating an experimental decay constant thatdepends on tissue characteristics (e.g. actual cell types, celldensities, cell sizes and effects of sample preparation and/or samplestaining) and input from acoustic monitoring device 102; and acorrelation module 114 for correlating (e.g. comparing) the experimentaland modeled TOF data, determining a diffusivity constant for the tissuesample based on a minimum of an error function of the correlation, usingthe determined diffusivity constant in the modelling module 112 alongwith candidate porosity values for the tissue sample to generate secondmodel TOF signals, and again using the correlation module 114 to make asecond correlation between the second model TOF signals based on thedetermined diffusivity constant and candidate porosities for the sampleand the experimental TOF data, determining a porosity of the tissuesample based on a minimum of an error function of the second correlationbetween the experimental TOF data and the model TOF signals generatedusing the determined diffusivity constant, and calculating based on theexperimental TOF signal, the determined diffusivity constant and thedetermined porosity, a concentration of a reagent within the sample at aparticular point in space and time.

These and other operations performed by these modules may result in anoutput of quantitative or graphical results to a user operationscomputer 101. Consequently, although not shown in FIG. 1, computer 101may also include user input and output devices such as a keyboard,mouse, stylus, and a display/touchscreen.

As described above, the modules include logic that is executed byprocessor 105. “Logic”, as used herein and throughout this disclosure,refers to any information having the form of instruction signals and/ordata that may be applied to affect the operation of a processor.Software is one example of such logic. Examples of processors arecomputer processors (processing units), microprocessors, digital signalprocessors, controllers and microcontrollers, etc. Logic may be formedfrom signals stored on a computer-readable medium such as memory 110that, in an exemplary embodiment, may be a random access memory (RAM),read-only memories (ROM), erasable/electrically erasable programmableread-only memories (EPROMS/EEPROMS), flash memories, etc. Logic may alsocomprise digital and/or analog hardware circuits, for example, hardwarecircuits comprising logical AND, OR, XOR, NAND, NOR, and other logicaloperations. Logic may be formed from combinations of software andhardware. On a network, logic may be programmed on a server, or acomplex of servers. A particular logic unit is not limited to a singlelogical location on the network. Moreover, the modules need not beexecuted in any specific order. Each module may call another module whenneeded to be executed.

In some embodiments, the acoustic monitoring device 102 may beretrofitted onto a commercial dip-and-dunk tissue processor such as theLynx II by Electron Microscopy Sciences®. In some embodiments, amechanical head designed using Solidworks® software may be fit aroundand seal a standard reagent canister. Once sealed, an external vacuumsystem may initiate to degas the bulk reagent as well as the contents ofthe cassette, including the tissue. In some embodiments, a cassetteholder designed for use with either a standard sized histologicalcassette such as CellSafe 5 by CellPath® or a biopsy capsule such asCellSafe Biopsy Capsules by CellPath® for smaller tissue samples may beutilized. Each holder would securely hold the tissue to prevent thesample from slipping during the experiment. The cassette holder may beattached to a vertical translation arm that would slide the cassetteholder in one direction. In some embodiments, the mechanical head may bedesigned with two metal brackets on either side of the tissue cassette,with one bracket housing 5 transmitting transducers, and the otherbracket housing 5 receiving transducers that are spatially aligned withtheir respective transmitting transducers. In some embodiments, thereceiving bracket may also house a pair of transducers orientedorthogonal to the propagation axis of the other transducers. After eachacquisition, the orthogonal sensors may calculate a reference TOF valueto detect spatiotemporal variations in the fluid that has a profoundeffect on sound velocity. Additionally, at the end of each 2Dacquisition, the cassette may be raised up and a second referenceacquisition acquired. In some embodiments, these reference TOF valuesmay be used to compensate for environmentally-induced fluctuations inthe formalin. Environmentally-induced fluctuations in the formalin orany other fixative may be, for example, temperature fluctuations in thecontainer comprising the porous material, vibrations, and others.

FIGS. 2A and 2B, respectively, depict examples of ultrasound scanpatterns from a biopsy capsule and from a standard-sized cassette. Themeasurement and modeling procedures described herein for a tissuesamples may likewise be applied on other forms of porous material. Assuch, while the present disclosure may illustrate modeling in thecontext of a tissue sample, such examples are non-limiting and thetechniques may be applied to other materials, such as any porousmaterial.

As described herein, the measurements from the acoustic sensors in anacoustic monitoring device may be used to track the change and/or rateof change of a TOF of acoustic signals through the tissue sample. Thisincludes monitoring the tissue sample at different positions (e.g. aplurality of different positions, such as at least 2 differentpositions, such as at least 3 different positions, such as at least 4different positions, such as at least 8 different positions) over timeto determine diffusion over time or a rate of diffusion.

For example, the “different positions,” also referred to “candidatediffusivity positions” may be a position within or on the surface of thetissue sample. According to some embodiments, the sample may bepositioned at different “sample positions” by a relative movement ofbiopsy capsule and acoustic beam path. The relative movement maycomprise moving the receiver and/or the transducer for “scanning” overthe sample in a stepwise or continuous manner. Alternatively, thecassette may be repositioned by means of a movable cassette holder.

For example, to image all the tissue in the cassette, the cassetteholder may be sequentially raised ≈1 mm vertically and TOF valuesacquired at each new position, as depicted in FIGS. 2A and 2B. Theprocess may be repeated to cover the entire open aperture of thecassette. Referring to FIG. 2A, when imaging tissue in the biopsycapsule 220, signals are calculated from all 5 transducers pairs,resulting in the scan pattern depicted in FIG. 2A. Alternatively, whenimaging tissue in the standard sized cassette 221 depicted in FIG. 2B,the 2nd and 4th transducer pairs may be turned off and TOF valuesacquired between the 1st, 3rd, and 5th transducer pairs located at therespective centers of the three middle subdivisions of the standardsized cassette 221. In some embodiments, two tissue cores may then beplaced in each column, one on the top and one on the bottom, enablingTOF traces from 6 samples (2 rows×3 columns) to simultaneously beobtained and significantly decreased run to run variation and increasedthroughput. In this exemplary embodiment, the full-width-half-maximum ofthe ultrasound beam is 2.2 mm.

In some embodiments, acoustic sensors in the acoustic monitoring devicemay include pairs of 4 MHz focused transducers such as the TA0040104-10by CNIRHurricane Tech (Shenzhen) Co., Ltd.® that are spatially aligned,with a tissue sample being placed at their common foci. One transducer,designated the transmitter, may send out an acoustic pulse thattraverses the coupling fluid (i.e. formalin) and tissue and is detectedby the receiving transducer.

FIG. 2C shows a timing diagram for an exemplary embodiment of thesubject disclosure. Initially, the transmitting transducer can beprogrammed with a waveform generator such as the AD5930 by AnalogDevices® to transmit a sinusoidal wave for several hundred microseconds.That pulse train may then be detected by the receiving transducer aftertraversing the fluid and tissue. The received ultrasound sinusoid andthe transmitted sinusoid may be compared using, for instance, a digitalphase comparator such as the AD8302 by Analog Devices. In someembodiments, the output of the phase comparator yields a valid readingduring the region of temporal overlap between the transmitted andreceived pulses. The output of the phase comparator is allowed tostabilize before the output is queried with an integrated analog todigital converter on the microcontroller, such as the ATmega2560 byAtmel®. The process may then be repeated at multiple acousticfrequencies across the bandwidth of the transducer to build up the phaserelationship between the input and output sinusoids across a frequencyrange. This acoustic phase-frequency sweep is directly used to calculatethe TOF using a post-processing algorithm analogous to acousticinterferometry and capable of detecting transit times withsub-nanosecond accuracy.

In some embodiments, the “measured TOF”, i.e. the “measured TOF value”obtained for a particular time point and a particular candidatediffusivity point is computed from a measured phase shift between atransmitted ultrasound signal and the corresponding received ultrasoundsignal, whereby the beam path of the ultrasound signal crossed theparticular candidate diffusivity point and whereby the phase shift wasmeasured at the particular time point.

FIG. 3 shows a method for obtaining a diffusivity coefficient for atissue sample, according to an exemplary embodiment of the subjectdisclosure. The operations disclosed with respect to this embodiment maybe performed by any electronic or computer-based system, including thesystem of FIG. 1. In some embodiments, the operations may be encoded ona computer-readable medium such as a memory and executed by a processor,resulting in an output that may be presented to a human operator or usedin subsequent operations. Moreover, the operations may be performed inany order besides the order disclosed herein, provided the spirit of thesubject disclosure is maintained.

In some embodiments, the method includes calculating an acousticvelocity for the tissue sample (S330). This operation includescalculating a speed of sound in the reagent that the tissue sample isimmersed in. For example, a distance between ultrasound transducersd_(sensor) i.e., the distance between the transmitting transducer andthe receiving transducer, may be accurately measured, and a transit timet_(reagent) between the ultrasound transmitter and the ultrasoundreceiver in pure reagent is measured, with the speed of sound in thereagent r_(reagent) being calculated using:

$r_{reagent} = \frac{d_{sensor}}{t_{reagent}}$

In some embodiments, the tissue thickness may also be obtained viameasurement or user input. A variety of suitable techniques areavailable to obtain tissue thickness, including ultrasound, mechanical,and optical methods. Finally, the acoustic velocity is determined (S330)by obtaining the phase retardation from the undiffused tissue (i.e., atissue sample to which the fixation solution has not been applied yet)with respect to the bulk reagent (e.g. the fixation solution) using:

Δt = t_(tissue + reagent) − t_(reagent)  and$\frac{1}{r_{tissue}\left( {t = 0} \right)} = {\frac{1}{r_{reagent}} + \frac{\Delta \; t}{d_{tissue}}}$

In some embodiments, the specific equation is derived based on the knowngeometry of the tissue sample and, generally, this equation representsthe speed of sound in the undiffused tissue sample (i.e. a tissue samplelacking the reagent, e.g. lacking the fixation solution) at a time t=0.In the experimental embodiment, for example, the acoustic velocity of atissue sample may be calculated by first calculating the speed of soundin the reagent based on the distance between the two ultrasoundtransducers (that are herein also referred to as “sensors”) (d_(sensor))being accurately measured as with a calibrated caliper. In this example,the sensor separation was measured with a caliper and sensor separationd_(sensor)=22.4 mm. Next the transit time (t_(reagent)) required for anacoustic pulse to traverse the reagent (lacking the tissue) between thesensors may be accurately recorded with an applicable program. In theexperimental example, t_(reagent)=16.71 μs for a bulk reagent of 10% NBF(neutral buffered formalin). The sound velocity in the reagent(r_(reagent)) may then be calculated as:

$r_{reagent} = {\frac{d_{sensor}}{t_{reagent}} = {\frac{22.4\mspace{14mu} {mm}}{16.71\mspace{14mu} {\mu s}} \approx {1.34\mspace{14mu} {{mm}/{\mu s}}}}}$

In this experiment, a sample piece of tonsil was cored with a 6 mmhistological biopsy core punch to ensure accurate and standardizedsample thickness (d_(tissue)=6 mm), and the TOF differential (Δt) wascalculated between the acoustic sensors with the tissue present(t_(tissue+reagent)) and without the tissue present (t_(reagent)):

Δt=t _(tissue+reagent) −t _(reagent)

Δt=16921.3−16709.7=211.6 ns

The time t_(reagent) is the time required by an ultrasound signal fortraversing the distance from the transmitting transducer to thereceiving transducer, whereby the signal passes a reagent volume but notthe tissue sample. Said traversal time can be measured e.g. by placing abiopsy capsule between the two sensors that has the same diameter as thetissue, e.g. 6 mm, and performing a TOF measurement for a signal thatpasses solely the reagent, not the tissue.

The time t_(tissue) is the time required by an ultrasound signal fortraversing the distance from the transmitting transducer to thereceiving transducer, whereby the signal passes the tissue sample thatdoes not comprise and is not surrounded by the reagent. Said traversaltime can be measured e.g. by placing a biopsy capsule between the twosensors before adding the reagent to the capsule and performing a TOFmeasurement for a signal that passes solely the tissue.

The time differential (or “TOF differential”) Δt caused by the tissue inaddition to the tissue's thickness and the speed of sound in the reagentmay be used to calculate the sound velocity of the undiffused tissue(t_(tissue)(t=0)) with the following equation derived from the knowngeometry (e.g. cylinder-shape, cube-shaped, box-shaped, etc.) of thesample:

$\frac{1}{r_{tissue}\left( {t = 0} \right)} = {\left. {\frac{1}{1.34\mspace{14mu} {{mm}/{\mu s}}} + \frac{0.2116\mspace{20mu} {\mu s}}{6\mspace{14mu} {mm}}}\Rightarrow{r_{tissue}\left( {t = 0} \right)} \right. = {1.28\mspace{14mu} {{mm}/{\mu s}}}}$

Subsequently, a modeling process is executed to model the TOF over avariety of candidate diffusivity constants. The candidate diffusivityconstants comprise a range of constants selected (S331) from known orprior knowledge of tissue properties obtained from the literature. Thecandidate diffusivity constants are not precise but are simply based ona rough estimate of what the range may be for the particular tissue ormaterial under observation. These estimated candidate diffusivityconstants are provided to the modeling process (steps S332-S335), with aminimal of an error function being determined (S337) to obtain the truediffusivity constant of the tissue. In other words, method tracksdifferences between the experimentally measured TOF diffusion curve anda series of modeled diffusion curves with varying diffusivity constants.

For example, upon selecting one of a plurality of candidate diffusivityconstants, the spatial dependence of the reagent concentration in thetissue sample is simulated (S332), based on a calculation of the reagentconcentration C_(reagent) as a function of time and space, using thesolution to a heat equation for a cylindrical object:

${c_{reagent}\left( {t,D,x} \right)} = {c_{\max}\left( {1 - {2{\sum\limits_{n = 1}^{\infty}\; \frac{e^{{- {D\alpha}_{n}^{2}}{t/R_{0}^{2}}}{J_{0}\left( {\alpha_{n}{x/R_{0}}} \right)}}{\alpha_{n}{J_{1}\left( \alpha_{n} \right)}}}}} \right)}$

where x is the spatial coordinate in the depth direction of the tissue,Ro is the radius of the sample, D is the candidate diffusivity constant,t is time, Jo is a Bessel function of the first kind and 0th order, J1is a Bessel function of the first kind and 1st order, αn is the locationof the nth root of a 0th order Bessel function, and c_(max) is themaximum concentration of the reagent. In other words, the summation ofthe coefficient of each of these Bessel functions (higher-orderdifferential equations), provides the constant as a function of space,time, and rate, i.e. the diffusivity constant. Although this equation isspecific to the cylindrical tissue sample disclosed in theseexperimental embodiments, and the equation would change depending on theshape or boundary condition, the solution to the heat equation for anyshape may provide the diffusivity constants for that shape. For example,heat equations for object having spherical, cubic or rectangular blockshapes can also be utilized in the disclosed methods.

In some embodiments, this step is repeated for a plurality of timepoints (S333-S334) to obtain a time-varying TOF (that corresponds to anexpected reagent concentration because the integral of the expectedreagent concentration at a particular time point can be used forcomputing the speed of sound differential) (S335). For example, the stepmay be repeated for at least 2 time points, for at least 3 time points,for at least 4 time points, or for at least 8 time points. For example,a determination is made as to whether or not the diffusion time iscomplete. This diffusion time may be based on the hardware or the typeof system being used. For each time interval T, steps S333, S334, andS332 are repeated until the modeling time is complete upon which themodeled reagent concentration is converted to a time-varying TOF signal(S335).

In the experimental embodiment, each of the used candidate diffusionconstants D_(candidate) is contained in the following value range:

0.01≤D _(candidate)≤2μm²/ms

In some embodiments, the tissue sample was cored with a cylindricalbiopsy core punch and therefore may be well approximated by a cylinder.In some embodiments, the solution to the heat equation above was thenused to calculate an expected concentration of the reagent (c_(reagent))in the tissue sample and, for the first time point in the experiment,i.e. after 104 seconds of diffusion (based on the time interval betweenTOF acquisitions used in the system performing the disclosedexperiment), the solution representing the concentration of the reagentin the depth direction of the tissue is depicted in FIG. 5A. Forexample, a particular system may regularly measure a new TOF value foreach of a number of different spatial locations which here are alsoreferred to as “pixels”. Each “pixel” may thus have an update rate ofassigning a new TOF value, e.g. every 104 seconds.

FIG. 5A shows the simulated concentration gradient of 10% NBF into anabout 6 mm sample of tissue after about 104 seconds of passive diffusionas calculated from the heat equation in the experimental embodiment.Moreover, these steps were repeated to determine the concentration ofthe reagent throughout the tissue repeatedly every 104 s over the courseof the experiment (8.5 hours long in the experimental embodiment), andthe result depicted in FIG. 5B.

FIG. 5B shows a plot of creagent (t, r) displaying the (“expected”,“modeled”, or “heat equation based”) concentration of the reagent at alllocations in the tissue (horizontal axis) as well as at all times(curves moving upward).

Referring back to FIG. 3, the results of the reagent modeling steps(S332-S334) may be used to predict the contribution towards theultrasound signal based on the fact that the ultrasound detectionmechanism linearly builds up phase retardation over the depth of thetissue.

In some embodiments, since the ultrasound detects an integrated signalfrom all tissue in the depth direction, i.e. along the propagation axisof the US beam and will thus be sensitive to the integrated amount offluid exchange in the depth direction, an “integrated expected” reagentconcentration c_(detected), also referred to as “detected reagentconcentration”, may be calculated. The “detected reagent concentration”is thus not an empirically detected value. Rather, it is a derivativevalue created by spatially integrating all expected reagentconcentrations computed for a particular time point t and for aparticular candidate diffusivity constant. The spatial integration maycover, for example, the radius of the tissue sample.

For example, the detected reagent concentration c_(detected) may becalculated using:

${c_{detected}(t)} = {\frac{2}{R_{0}}{\int_{0}^{R_{0}}{{c_{reagent}\left( {t,x} \right)}{dx}}}}$

In some embodiments, the integrated reagent concentration c_(detected)is used to calculate the total amount of reagent at a particular timepoint. For example, additional volume and/or weight information of thesample may be used for calculating absolute reagent amounts.Alternatively, the reagent amount is computed in relative units, e.g. asa percentage value indicating e.g. the volume fraction [%] of the samplebeing already diffused by the reagent.

After simulating (i.e., computing based on the heat equation model) thedetected concentration of the reagent for a given candidate diffusivityconstant and a given time point, that detected concentration may then beconverted into a TOF signal (S335) as a linear combination of undiffusedtissue and reagent, using:

${{TOF}_{tissue}\left( {t,D} \right)} = \frac{d_{tissue}}{{r_{tissue}\left( {t = 0} \right)} + {{{\rho c}_{detected}(t)}\left( {{r_{tissue}\left( {t = 0} \right)} - r_{reagent}} \right)}}$

where r_(tissue)(t=0) is the speed of sound of undiffused tissue, and ρis the volume porosity of the tissue, representing the fractional volumeof the tissue sample that is capable of fluid exchange with the bulkreagent. This equation therefore models the change in TOF signal fromdiffusion as a linear combination of the two distinct sound velocities(tissue and reagent). As the TOF of the respective sound velocities ofpure tissue on the one hand and pure reagent on the other hand caneasily be determined empirically (e.g. by respective phase-shift basedTOF measurements), the amount of the reagent having already diffusedinto the sample at the particular time point can easily be determined.

In some embodiments, the TOF contribution of the pure tissue sample(being free of the TOF contribution of a bulk fluid such as samplebuffers or the tissue fluid) can be obtained by subtracting the TOFcontribution measured for the tissue sample including and/or beingsurrounded by the bulk fluid from the TOF contribution measured for anultrasound signal having traversed a corresponding inter-transducerdistance filled with said bulk fluid only.

FIGS. 6A and 6B respectively depict a plot of the simulated, “detected”or “integrated” concentration of NBF by the ultrasound over the courseof the experiment (FIG. 6A), and a plot of the simulated (or “expected”)TOF signal for the first candidate diffusivity constant (FIG. 6B, whereD=0.01 μm2/ms). The TOF signals in FIG. 6B are computed as derivativesof the respective integrated concentration of the reagent.

At this point, the method generally correlates (S336) the modeled (or“simulated” or “expected”) TOF with an experimental TOF determined bymeasuring different spatial regions of interest (ROIs), also referred toas “candidate diffusivity points”, within the tissue sample anddetermining a minimum of an error function to obtain a true diffusivityconstant. In this example, each modeled TOF for the specific diffusionconstant selected in the range specified by (S322) is correlated withthe experimental TOF (S336), and determination is made as to whether ornot an error is minimized (S337). If the error is not minimized, thenext diffusion constant is selected (S338) and the modeling process(S332-S335) is repeated for the new diffusion constant. If it isdetermined that the error is minimized (S337) based on correlation(S336), then the true diffusivity constant is determined (S339) and themethod ends.

FIG. 4 shows an alternative method whereby all candidate diffusivityconstants are first used to perform the modeling, based on stepsS446-S447 and the correlation (S448) is performed after all thediffusivity constants are processed. A depiction of the temporallyvarying TOF signal calculated for all potential diffusivity constants isshown in FIG. 7. For example, FIG. 7 depicts simulated TOF traces overthe 8.5 hour experiments for 6 mm tissue samples with diffusivityconstants ranging from 0.01 to 2.0 μm2/ms. In the embodiment of FIG. 4,the error minimization is performed within true diffusivity constantdetermination step S439.

In either case, the experimental TOF must be determined for thecorrelation to take place. In some embodiments, the experimental TOF maybe determined by measuring different spatial regions of interest (ROIs)within the tissue. Each signal has the contribution from backgroundreagent subtracted out to isolate the contribution from active diffusioninto the tissue. Individual TOF trends are temporally smoothed viafiltering. These spatially distinct TOF trends are thenspatially-averaged to determine the average rate of 10% NBF diffusioninto the tissue.

FIGS. 8A and 8B respectively depict experimentally calculated TOF trendscollected from a 6 mm piece of human tonsil sample (FIG. 8A) andspatially-averaged TOF signals (FIG. 8B) representing the average rateand amount of fluid exchange of 10% NBF into the tissue.

The average rate of diffusion into the tissue is highly correlated to asingle exponential signal (depicted by the dashed line in FIG. 8B), andderived by:

TOF_(experimental)(t)=Ae ^(−t/τ) _(experimental)+offset

where A is the amplitude of the TOF in nanoseconds (i.e., the TOFdifference between the undiffused and fully diffused tissue sample),τ_(experimental) is the sample's decay constant representing the timerequired for the TOF to decay to 37% of its amplitude or equivalently tobe 63% decayed and offset is a vertical offset of the above given decayfunction.

The 63% can be derived by the following calculation: at time t=τ,TOF(τ)=Ae(−tau/tau)=Ae−1=A/e=A/2.72=0.37*A.

In some embodiments, it is assumed that the TOF decreases with anincrease in reagent concentration in the sample, but the method wouldlikewise be applicable for reagents which increase the measured TOF upondiffusing into the sample. In the 6 mm piece of human tonsil of theexperimental embodiment, τ_(experimental)=2.83 hours. Thus, from aplurality of TOFs having been experimentally determined for a pluralityof consecutive time points, a decay constant of the tissue sample can becomputed, e.g. by plotting the amplitudes of the TOF signal over time,analyzing the plot for identifying the offset and resolving the abovesolution for the decay constant.

In some embodiments, the error correlation (S336 in FIG. 3, S448 in FIG.4) is performed to determine an error of the modeled (“expected”) TOFvs. the experimental TOF. Having calculated simulated and experimentalTOF signals, a difference between the two signals may be calculated tosee whether or not the candidate diffusivity constant minimizes thedifference between the two signals (S337).

In some embodiments, the error function may be computed in differentways, for instance, using one of the following equations:

${{Error}(D)} = {\frac{1}{N}{\sum\limits_{t = 1}^{N}\; \left( {{{TOF}_{simulated}\left( {t,D} \right)} - {{TOF}_{experimental}(t)}} \right)^{2}}}$Error(D) = (τ_(simulated)(D) − τ_(experimental))²

In some embodiments, the first error function calculates thepoint-by-point difference between simulated (“modeled”, “expected”) andexperimentally measured TOF signals.

In some embodiments, the second error function exclusively compares therate of diffusion between the simulated and modeled TOF signal bycalculated the sum-squared differences between each's decay constant. Insome embodiments, the experimental decay constant τ_(experimental) canbe obtained experimentally as described above. In some embodiments, the“modeled”, “expected” or “simulated” decay constant τ_(simulated) can bederived analogously from the modeled (“expected”) TOFs signal ofconsecutive time points which also follow a decay function.

In some embodiments, based on the output of the error function, a truediffusivity constant may be determined (S339). In some embodiments, thetrue diffusivity constant is calculated as the minimum of the errorfunction, for instance:

D _(reconstructed)=arg min(error(D))

This equation enables a determination of the candidate diffusivitycoefficient that produce a TOF signal as close as possible to theexperimental data.

For example, with respect to the method depicted in FIG. 3, the errorfunction may be determined for each candidate diffusivity constant untilthe error is minimized (S337). Alternatively, in the method of FIG. 4,the correlation with experimental TOF may be performed after allcandidate diffusivity constants are processed, upon which thedetermination (S439) of the true diffusivity constant includesdetermining a minimum of the error function. In some embodiments, theminimum of the error function is ideally zero, or as close as possibleto zero. Any error function known in the art may be used with the goalof minimizing the error between the modeled versus experimentalcoefficients disclosed herein.

FIGS. 9A and 9B respectively show a plot of the calculated errorfunction between simulated and experimentally measured TOF signals as afunction of candidate diffusivity constant (FIG. 9A, ΔD≈10^(e-5)μm²/ms.), and a zoomed-in view of the error function (FIG. 9B). In theexperimental embodiment, the minimum of the error function wascalculated to be at D=0.1618 μm²/ms. The validity of the reconstructedconstant was tested and used to back-simulate a TOF trend. FIG. 10depicts the TOF trend calculated with this diffusivity constant andplotted alongside the experimental TOF measured with the 6 mm piece ofhuman tonsil. In FIG. 10, the plot shows the experimentally calculatedTOF trend from a 6 mm piece of human tonsil in 10% NBF (dotted line) andthe modeled TOF trend for D_(reconstructed)=0.168 μm²/ms (solid line).In this embodiment, τ_(experimental)=2.830 hrs and τ_(simulated)=2.829hrs.

Furthermore, this same procedure was repeated for several specimens of 6mm human tonsil samples, with successfully reconstructed diffusivityconstants for all samples, as depicted in FIGS. 11A and 11B. FIG. 11Ashows reconstructed diffusivity constants for the 23 samples of 6 mmhuman tonsil. Line 1151 represents the average. FIG. 11B shows a box andwhisker plot displaying the distribution of the reconstructeddiffusivity constants. Line 1152 represents the median value, and thebox 1153 extends from the 25-75 percentiles, with whiskers 1154extending from the 5-95 percentiles. Overall, the algorithm predicted 6mm tonsils samples have an average diffusivity constant of 0.1849 μm2/mswith a relative tight distributed producing a standard deviation of0.0545 μm2/ms.

FIG. 12A shows a system for monitoring the time-of-flight of anultrasound signal according to embodiments of the disclosure. In someembodiments, the ultrasound-based time-of-flight (TOF) monitoring systemmay comprise one or more pairs of transducers (e.g. TA0040104-10,CNIRHurricane Tech) for performing the time-of-flight measurements basedon a phase shift of the ultrasound signals. In the embodiment depictedin FIG. 12A, the system comprises at least one pair of transducersconsisting of an ultrasound (“US”) transmitter 902 and an ultrasoundreceiver 904 which are spatially aligned to each other such that atissue sample 910 which is placed in the beam path 914 from thetransmitter to the receiver is located at our close to the common fociof said two transducers 902, 904. The tissue sample 910 can becontained, for example, in a sample container 912 (e.g. a standardhistological cassette like “CellSafe 5” of CellPath or a biopsy capsulelike “CellSafe Biopsy Capsules” of CellPath) that is filled with afixation solution. Phase-shift based TOF measurements are performedbefore and after the biopsy capsule 912 is filled with the fixationsolution and while the solution slowly diffuses into the sample. The onetransducer acting as the transmitter sends out an acoustic pulse thattraverses the tissue and is detected by the other transducer acting asthe receiver. The total distance between two transducers constituting atransmitter-receiver transducer pair is referred to as “L”. The totaltime the ultrasound signal needs to traverse the distance between thetransmitter 902 and the receiver 904 may be referred to astime-of-flight of said signal. The transmitter 902 may be focused, forexample, at about 4 MHz and support a frequency sweep range of betweenabout 3.7 and about 4.3 MHz.

In some embodiments, the distance L is assumed to be known, at leastapproximately. For example, the distance of the transducers may beaccurately measured (e.g. by optic, ultrasound based or othermeasurement techniques) or may be disclosed by a manufacturer of theacoustic monitoring system.

The transmitting transducer 902 is programmable with a waveformgenerator (e.g. AD5930 from Analog Devices) to transmit a sinusoidalwave (or “sinusoidal signal”) for a defined frequency for a defined timeinterval, e.g. several hundred microseconds. That signal is detected bythe receiving transducer 904 after traversing the fluid and/or tissue.The received ultrasound signal 922 and the emitted (also referred to as“transmitted”) sinusoid signal 920 are compared electronically with adigital phase comparator (e.g. AD8302, Analog Devices).

A “received” “signal” (or wave) as used herein is a signal whoseproperties (phase, amplitude, and/or frequency, etc.) are identified andprovided by a transducer, e.g. receiver 904, that receives said signal.Thus, the signal properties are identified after said signal has passeda sample or any other kind of material.

A “transmitted” or “emitted” “signal” (or wave) as used herein refers toa signal whose properties (phase, amplitude, and/or frequency, etc.) areidentified by a transducer, e.g. transmitter 902 that emits the signal.Thus, the signal properties are identified before the signal has passeda sample or any other kind of material.

For example, the transmitted signal may be characterized by signalproperties identified by the transmitting transducer, the receivedsignal may be characterized by signal properties measured by thereceiving transducer, whereby the transmitting and the receivingtransducer are operatively coupled to a phase comparator of the acousticmonitoring system.

FIG. 12B depicts the determination of the TOF for the pure reagent fromwhich the speed of the sound wave for the beam path crossing the purereagent without the sample can be inferred. In this embodiment, the oneor more transducer pairs 902, 904 and the sample container 912 can bemoved relative to each other. Preferentially, the system comprises acontainer holder capable of repositioning the container 912 such thatthe US beam traverses a region 914 of the container that solelycomprises the fixation solution but not the tissue.

At a time, A, when the tissue is not yet immersed in a fixationsolution, the TOF for a sound signal traversing the distance between thetransducers is obtained via a measured phase shift φ_(exp) as describedfor FIG. 12A. In this case, the beam path crosses a sample being free ofthe reagent. As L is known, the measured TOF can be used for computingthe speed of the sound signal for traversing the distance in thepresence of the undiffused sample.

At a time, B, when the tissue is immersed in a fixation solution, theTOF for a sound signal traversing the distance between the transducersis obtained via a measured phase shift φ_(exp). In this case, the beampath crosses a sample container comprising only the reagent, not thesample (or crosses the sample container at a position that is free ofthe sample). As L is known, the measured TOF can be used for computingthe speed of the sound signal for traversing the distance in thepresence of the reagent (and the sample container) only, i.e., in theabsence of the sample in the beam path.

Time A and time B may represent identical time points in case a furthertransducer pair is configured for performing the two measurements inparallel.

III. EXAMPLES

An investigation of the disclosed method of determining reagentconcentrations across space and time within a sample, and across tissuesample types, was conducted. Samples were monitored during coldimmersion in NBF using a TOF system as described above and extractedexperimental TOF data over time was obtained. Following TOF analysis,samples were warmed to fix the tissues and then processed in a tissueprocessor to prepare sample paraffin blocks. Blocks were sliced on amicrotome and mounted on microscope slides and stained according tostandard protocols, and in some instances read by qualified slidereaders to assess stain quality.

FIG. 13 shows a model of diffusion of a reagent into a cylindricalobject, such as a cylindrical tissue core. As can be seen, the reagentconcentration rapidly increases first at the edges of the tissue sample,and that the concentration of the reagent at the center increases slowly(if at all) at first, lagging the concentration changes seen at theedges of the sample, and then accelerating at later time points, beforebeginning to slow again. In this model:

TOF∞∫c(reagent)

In comparison to FIG. 5B, the changes in concentration over time aremore variable in rate than are the changes seen for percent diffused.This is not unexpected as percent diffusion is a measured average acrossthe entire sample, whereas the concentration changes are locationspecific. Furthermore, since sample porosity scales with A in thefollowing equation:

TOF_(experimental)(t)=Ae ^(−t/τ) ^(experimental) +offset,

once the diffusivity constant is known, candidate porosities can be usedto calculate simulated TOF curves and compared to experimental TOFcurves to generate an error, which error can be minimized. The errorfunction may be computed in different ways, for instance, using one ofthe following:

${{Error}({porosity})} = {\frac{1}{N}{\sum\limits_{t = 1}^{N}\left( {{{TOF}_{simulated}\left( {t,{porosity}} \right)} - {{TOF}_{experimental}(t)}} \right)^{2}}}$     Error(D) = (τ_(simulated)(porosity) − τ_(experimental))²

The first error function calculates the point-by-point differencebetween simulated (“modeled”, “expected”) and experimentally measuredTOF signals.

The second error function exclusively compares the rate of diffusionbetween the simulated and modeled TOF signal by calculating thesum-squared differences between each's decay constant. The experimentaldecay constant τ_(experimental) can be obtained experimentally asdescribed above. The “modeled”, “expected” or “simulated” decay constantτ_(simulated) can be derived analogously from the modeled (“expected”)TOFs signal of consecutive time points which also follow a decayfunction.

Based on the output of the error function, a true porosity may bedetermined. The true porosity is calculated as the minimum of the errorfunction, for instance:

ρ_(reconstructed)=arg min(error(porosity))

Once the porosity of the sample is determined, a concentration of areagent at a particular point in space and time can be calculated usingthe following equation:

${reagent\_ conc} = {\left( {\% \mspace{14mu} {diffused}} \right)(\rho)\left( \frac{MWg\_ reagent}{1\mspace{14mu} {liter}} \right)\left( \frac{1\mspace{14mu} {mol}}{MWg\_ reagent} \right)}$

FIG. 14 shows for comparison a typical distribution of the percentdiffusion of a formalin solution into the centers of tonsil tissue coresamples (approximately, 6 mm cylinders) at 3 hours and 5 hours, whereina 3 hour immersion of a sample yields decent staining whereas a 5 hourimmersion yields “ideal” staining. On average, a sample subjected to a 3hour immersion will reach a 52.6% percent diffusion at tissue center anda sample subjected to a 5 hour immersion will reach an average percentdiffusion of 76.9% diffused. The 95% predictive interval at 5 hoursindicates that a sample needs to be at least 52.45% diffused at thecenter to achieve “ideal” staining as judged by pathologist review.

FIG. 15 shows for comparison an ROC curve of staining quality(sensitivity and specificity) based on percent diffusion at the tissuesample center. In this instance, using percent diffusion at tissuecenter yields an area under the curve (AUC) of 0.8926 for prediction ofstaining quality based on a measurement of percent diffused at tissuecenter.

FIG. 16 shows for comparison a typical graph of the differential inpercent diffusion measured at the tissue sample center between about 3hours and about 5 hours of exposure to a reagent, with the result thatthe average difference between about 3 hours and about 5 hours ofdiffusion is about 24.3% at the center of the tissue.

Turning now to results obtained using the disclosed method ofdetermining reagent concentrations at particular spatial points within atissue sample from TOF data, FIG. 17 shows a raw data distribution ofdetermined tonsil tissue volume porosities for several samples. FIG. 18shows a corresponding box and whisker distribution of the data of FIG.17 for determined tonsil tissue volume porosities. As can be seen,tonsil tissue in particular exhibits an average porosity of about 0.15.

FIG. 19 shows a typical distribution of formaldehyde concentrations atthe tissue sample center for tonsil tissue core samples (approximately 6mm cylinders) at 3 hours and 5 hours, wherein an about 3 hour immersionof a sample yields decent staining whereas a 5 hour immersion yields“ideal” staining. On average, a sample subjected to an about 3 hourimmersion will reach a 92.3 mM formaldehyde concentration at tissuecenter and a sample subjected to a 5 hour immersion will reach anaverage concentration at tissue center of 137.5 mM. The 95% predictiveinterval at 5 hours indicates that a sample should have achieved atleast 91.07 mM formalin at tissue center during fixation to achieve“ideal” staining as judged by pathologist review.

FIG. 20 shows an ROC curve of staining quality (sensitivity andspecificity) based on formaldehyde concentration at the tissue samplecenter. The AUC in this case is 0.9256, which demonstrates thesuperiority of using formaldehyde concentration at tissue center as apredictor of stain quality in comparison with use of percent diffused attissue center as a predictor of stain quality (AUC−0.8926) as was shownin FIG. 15.

Likewise, FIG. 21 demonstrates the superiority of reagent concentrationat tissue center as a predictor of stain quality. It shows a graph ofthe differential in formaldehyde concentration at the tissue samplecenter between about 3 hours and about 5 hours of immersion in an NBFsolution. Overall, the average difference seen in concentration is 45mM. Compared to the difference in percent diffused (24%; FIG. 16), thedifference in concentration at tissue center between about 3 about andabout 5 about is more dramatic at about 33% (45 mM/137 mM×100%)reflecting the differences in reagent concentration occurring late in animmersion that can have an effect on staining quality at the tissuecenter. Again, this demonstrates the advantage of using a method thatprovides a measure (in this case concentration) that is location andtime specific within the sample volume, as opposed to an average measureacross the entire sample volume (as in the case of a percent diffusedmeasurement alone).

Having established the disclosed method could be used to determine aporosity for tonsil tissue, porosities were measured for 10 differenttissue types (80 samples), and the results are shown in FIG. 22, whichshows the distributions of raw porosities for the several tissue types.FIG. 23 shows a set of box and whisker distributions of porosities forthe several tissue types. As can be seen, for most tissue types, theaverage porosity (line in box) is between about 0.1 and about 0.2,whereas skin has a much higher porosity of more than about 0.3.

For comparison, FIG. 24 shows the distributions of the determineddiffusivity constants for the several tissue types, and FIG. 25 shows aset of box and whisker distributions of the diffusivity constants forthe several tissue types. In comparison to the average porositiesdetermined among the several tissue types, the diffusivity constant ismore variable.

FIG. 26 shows the distributions of raw percent diffusion at the tissuesample center at 3, 5 and 6 hours determined for the several tissuetypes, and FIG. 27 shows a set of box and whisker distributions ofpercent diffusion at the tissue sample center at 3, 5 and 6 hours forthe several tissue types. FIG. 28 shows the distributions of rawformaldehyde concentration as determined at the tissue sample center at3, 5 and 6 hours for several tissue types, and FIG. 29 shows a set ofbox and whisker distributions of formaldehyde concentration at thetissue sample center at 3, 5 and 6 hours for several tissue types. Froma comparison of the raw data and box-and-whisker distributions based onmeasuring percent diffusion and those based on determining reagentconcentration at the center of the tissue, it can be seen that the datatend to cluster more tightly when concentration is utilized.

FIG. 30 shows distributions of raw formaldehyde concentrations at thetissue sample center for the several tissue types after the indicatedimmersion times, and FIG. 31 shows a set of box and whiskerdistributions of formaldehyde concentrations at the tissue sample centerfor the several tissue types after the indicated immersion times. Theseresults confirm the correlation of tissue center formaldehydeconcentrations above about 90 mM (such as above 100 mM) with “ideal”staining since earlier studies showed that fixation for at least 6 hours(5 hours for tonsil) in a cold step of a cold+hot fixation protocolensures “ideal” staining. The results were further confirmed throughmicroscopic analysis, with qualified readers determining the tissuesindicated in FIG. 32 indeed demonstrated “ideal (optimal)” stainingafter the indicated times.

FIG. 33 shows the raw distribution of formaldehyde concentration at thetissue sample center across all tissues types after 6 hours of immersionin 10% NBF, and FIG. 34 show the box and whisker distribution offormaldehyde concentration at the tissue sample center for all tissuesafter 6 hours of immersion in 10% NBF. The 90 mM (or 100 mM)formaldehyde concentration level for achievement of “ideal staining” isconfirmed across all tissue types. The difference between calculatingformaldehyde concentration at the center of the tissue based on TOF dataand simply using a standard fixation time protocol is that while a 6hour immersion might not be sufficient to achieve ideal staining forsample larger than 6 mm in diameter, a time sufficient to achieve atleast 90 mM (or 100 mM) formaldehyde at the tissue center will ensure“ideal” staining of the sample. Conversely, smaller samples (e.g. needlecore biopsies) that could be potentially be over-fixed using a standardfixation time of 6 hours can be treated only until the concentration attissue center reaches at least 90 mM, thus leading to a shorter overallanalysis time.

FIG. 35 shows an embodiment of the disclosed method for obtaining adiffusivity coefficient, a porosity, and formaldehyde concentration atthe tissue sample center. At S430 the acoustic velocity of the sample ismeasured as was previously described in the context of FIG. 3. Also likethe embodiment of FIG. 3, operations and decisions S431, S432, S433,S434, S435, S436, S437 and S438 are performed to define the diffusivityconstant. Once the diffusivity constant is determined at S439, a rangeof porosities that are used to model the diffusion of the reagentsolution into the sample is set at S440. The range can be set by defaultor entered by a user. For example, based on the experimentallydetermined porosity values discussed above in regard to FIG. 22, to arange of 0.05 to 0.50 (or a narrower) should cover most, if not all,tissue types. A narrower range can be set when the tissue type has beenexamined prior, and for example, the user can enter the tissue type toprovide an appropriate range of values for the model to explore. AtS441, S442 and S443, the diffusivity constant from S439 and a candidateporosity set at S440, are used to model the spatial dependence of thereagent over a series of time points T to T+n. The model built over theseries of time points is then used to generate an expected TOF curve atS444 and correlated with the experimental TOF curve at S445. At S446,the error between the expected and experimental TOF curves is checked tosee if it is at a minimum, and if so, the candidate tissue porosity isdetermined at S448 to be the actual tissue porosity. If not, the processis repeated with a second candidate porosity at S447. Once both thediffusivity constant (S439) and the porosity (S448) are defined, aspatial model of reagent concentration across time can be generated atS449. Once the spatial model of reagent concentration over time isestablished, the concentration at a particular point within the sampleat a particular time, such as at sample center, can be extracted fromthe model.

IV. FURTHER EMBODIMENTS

In a further aspect, the disclosure relates to a system including anacoustic monitoring device that detects acoustic waves having traveledthrough a porous material and a computing device communicatively coupledto the acoustic monitoring device 102. The computing device includesinstructions which, when executed, cause the computing device to performoperations comprising:

(i) computing a set of experimental TOFs from measured acoustic data ofthe detected acoustic waves, each experimental TOF indicating the TOF ofacoustic waves that have traveled through a candidate diffusivity pointof the porous material at a respective one of a plurality of timepoints; the candidate diffusivity point is a location in or at thesurface of the porous material;

(ii) setting a range of candidate diffusivity constants for the porousmaterial;

(iii) for each of the candidate diffusivity constants, simulating aspatial dependence concentration model of an expected concentration of areagent within the porous material for the plurality of time points andfor the candidate diffusivity point, the expected concentration of thereagent being a function of time, space and said candidate diffusivityconstant;

(iv) using the spatial dependence concentration model for computing aspatial dependence TOF model for the porous material, the TOF modelassigning, to the candidate diffusivity point, for each of the pluralityof time points and for each of the candidate diffusivity constants, arespectively modeled TOF; the expressions “modeled”, “simulated” and“expected” are used herein interchangeably; for example, the “use” mayconsist of converting the spatial dependence concentration model to thespatial dependence TOF model; and

(v) determining an error function for the candidate diffusivity point,the error being indicative of a distance (that may also be considered asand referred to as an “error”) between each of the modeled TOFs assignedto said candidate diffusivity point from a corresponding experimentalTOF, the experimental TOF having been measured by the acousticmonitoring device at the same time point as used for modeling itscorresponding modeled TOF;

(vi) using the error function for identifying one or more modeled TOFshaving minimum distances to the corresponding experimental TOFs;

(vii) outputting a diffusivity constant calculated for the porousmaterial from the candidate diffusivity constants of the one or moreidentified modeled TOFs.

(viii) setting a range of candidate porosities for the porous material;

(ix) for each of the candidate porosities, simulating a spatialdependence concentration model of an expected concentration of a reagentwithin the porous material for the plurality of time points andoutputted diffusivity constant, the expected concentration of thereagent being a function of time, space, diffusivity constant and thecandidate porosity; and

(x) determining an error function for the candidate porosity, the errorbeing indicative of a distance (that may also be considered as andreferred to as an “error”) between each of the modeled TOFs assigned tosaid candidate porosity point from a corresponding experimental TOF, theexperimental TOF having been measured by the acoustic monitoring deviceat the same time point as used for modeling its corresponding modeledTOF.

In a further aspect, the disclosure relates to a corresponding method.

According to other embodiments, the computing the spatial dependence TOFmodel comprises determining each of the modeled TOFs by solving a heatequation for the porous material.

According to particular embodiments, the acoustic data comprises: thevelocity of the sound waves in the porous material prior to diffusionwith the reagent; and/or the experimental TOFs of the acoustic wavesthrough the porous material at the plurality of time points duringdiffusion of the reagent into the porous material; and/or experimentalphase shift data for computing the experimental TOFs from theexperimental phase shift data; and/or velocity of the sound waves in thereagent being free of the porous material; and/or a thickness of theporous material. For example, said thickness is determined, according toembodiments, using a pulse echo ultrasound.

According to other embodiments, the computation of the spatialdependence TOF model comprises:

(i) selecting a first one of a plurality of candidate diffusivityconstants;

(ii) calculating an expected reagent concentration c_(reagent) at eachof the plurality of candidate diffusivity points in the porous materialfor each of the plurality of time points in dependence of the selectedcandidate diffusivity constant;

(iii) calculating an integrated reagent concentration c_(detected) foreach of the plurality of time points and for each of the candidatediffusivity constants by integrating the expected reagent concentrationc_(reagent) calculated for said time point and said candidatediffusivity constant over a radius of the porous material;

(iv) converting the integrated reagent concentration to a modeled TOF ofthe spatial dependence TOF model by computing a linear combination ofthe speed of the sound waves in the porous material prior to diffusionwith the reagent and the speed of the sound waves in the reagent beingfree of the porous material; and

(v) selecting a next one of the candidate diffusivity constants andrepeating this step and the three previous steps for the next selectedcandidate diffusivity constant until a termination criterion is reachedto arrive at the diffusivity constant of the sample

(vi) selection a first one of a plurality of candidate porosities forthe porous material

(vii) calculating a second modeled TOF for the sample based on thediffusivity constant arrived at above and the first one of the pluralityof candidate porosities

(viii) selecting a next one of the candidate porosities for the porousmaterial and repeating this step and the previous step until atermination criterion is reached to arrive at the porosity of thesample; and

(ix) calculating an actual reagent concentration at each of thecandidate diffusivity points in the porous material

In summary, determination reagent concentrations with any samplematerial may be provided by calculating the speed of sound in a reagentat a given temperature, pressure, etc., determining the sample'sthickness with standard pulse echo ultrasound, determining the absolutesound velocity in the undiffused sample via phase retardation ofultrasound, followed by generating the modeled TOF trend from thecandidate diffusivity constant first simulating the spatial dependenceof the reagent diffusion into the sample, summing the total reagentconcentration detected by the ultrasound beam, converting the detectedreagent concentration to the TOF differential, and repeating these stepsfor multiple diffusion times. Then, the modeled TOF trend is determinedby repeating the spatial dependence simulation for a plurality ofcandidate diffusivity constants (such as in a range as provided by thoseknown from literature) and calculating an error between the experimentaland simulated TOF differentials at all times and for all diffusivityconstants, resulting in an error function between the experimental andmodeled TOF as a function of diffusivity constant. Calculating the truediffusivity constant as the minimum of the error function results in anoutput. Then, using the true diffusivity constant and a plurality ofcandidate porosities for the sample (such as selected from a range ofexpected tissue porosities) to generate a second modeled TOF trend overtime, calculating a second error function between the second modeled TOFtrend and the experimental TOF trend at all times, and calculating thetrue porosity of the sample as a minimum of second error function. Thetrue porosity can then be input along with the true diffusivity constantback into the model for spatial dependence of reagent diffusion toobtain reagent concentrations at any spatial point at any time within asample during the diffusion process. Alternatively, the reagentconcentration in units of molarity at a particular spatial point at aparticular time according to the following equation based on % Diffusedat a particular time.

Reagent_concentration=(%diffused)(porosity)(g reagent/L)(1 mole/MW ofreagent)

Moreover, the subject disclosure applies to both biological andnon-biological context, providing an ability to reconstruct thediffusivity constant of any substance based on the acoustic TOF curve.The disclosed methods are more sensitive and accurate when compared toprior art methods. Although the disclosed operations provide fitting theTOF curve to a single exponential function comprising a summation ofBessel functions, a double exponential or quadratic function may be moreappropriate, depending on the context. Therefore, the equation itselfmay change, while the novel features disclosed herein may maintain theirinventive spirit and scope when read by a person having ordinary skillin the art.

Diffusivity constant and porosity calculations are known to be usefulfor many applications, including compositional analysis. The presentsystems and methods are contemplated to be used in any system thatutilizes diffusivity constant and porosity measurements. In one specificembodiment, the present systems and methods are applied to the field ofmonitoring diffusion of fluids into porous materials.

In some embodiments, the porous material is a tissue sample. In manycommon tissue analysis methods, the tissue sample is diffused with afluid solution. For example, Hine (Stain Technol. 1981 March;56(2):119-23) discloses a method of staining whole tissue blocks byimmersing a tissue sample in a hematoxylin solution and eosin solutionafter fixation and prior to embedding and sectioning. Additionally,fixation is frequently performed by immersing an unfixed tissue sampleinto a volume of fixative solution, and the fixative solution is allowedto diffuse into the tissue sample. As demonstrated by Chafin et al.,(PLoS ONE 8(1): e54138. doi:10.1371/journal.pone. 0054138 (2013)), afailure to ensure that a fixative has sufficiently diffused into thetissue can compromise the integrity of the tissue sample. Thus, in oneembodiment, the present systems and methods are applied to determine asufficient time of diffusion of a fixative into a tissue sample. In sucha method, the user selects a minimum fixative concentration to beachieved at a particular point in the tissue sample (such as the centerof the thickness of the tissue sample). Knowing at least the tissuethickness, tissue geometry, and the calculated true diffusivity aminimum time to reach the minimum relative (to the surrounding fluid)fixative concentration at the center of the tissue sample can bedetermined. The fixative will thus be allowed to diffuse into the tissuesample for at least said minimum time. However, to extend this tomethods that can be used for real-time monitoring, determination of thetissue sample porosity as disclosed herein permits determination of anactual fixative concentration that needs to be achieved to ensure sampleintegrity. Thus, based on the system and method disclosed herein, othertechniques such as radiolabel tracing, mid-IR evaluation and MRI can beused to determine appropriate times for particular treatments withparticular reagents, such as fixatives.

In some embodiments, the systems and methods disclosed herein are usedin connection with a two-temperature immersion fixation method on atissue sample. As used herein, a “two-temperature fixation method” is afixation method in which tissue is first immersed in cold fixativesolution for a first period of time, followed by heating the tissue forthe second period of time. The cold step permits the fixative solutionto diffuse throughout the tissue without substantially causingcross-linking. Then, once the tissue has adequately diffused throughoutthe tissue, the heating step leads to cross-linking by the fixative. Thecombination of a cold diffusion followed by a heating step leads to atissue sample that is more completely fixed than by using standardmethods. Thus, in an embodiment, a tissue sample is fixed by: (1)immersing an unfixed tissue sample in a cold fixative solution andmonitoring diffusion of the fixative into the tissue sample bymonitoring TOF in the tissue sample using the systems and methods asdisclosed herein (diffusion step); and (2) allowing the temperature ofthe tissue sample to raise after a threshold TOF has been measured(fixation step). In exemplary embodiments, the diffusion step isperformed in a fixative solution that is below 20° C., below 15° C.,below 12° C., below 10° C., in the range of about 0° C. to about 10° C.,in the range of about 0° C. to about 12° C., in the range of about 0° C.to about 15° C., in the range of about 2° C. to about 10° C., in therange of about 2° C. to about 12° C., in the range of about 2° C. toabout 15° C., in the range of about 5° C. to about 10° C., in the rangeof about 5° C. to about 12° C., or in the range of about 5° C. to 1about 5° C. In exemplary embodiments, the environment surrounding thetissue sample is allowed to rise within the range of about 20° C. toabout 55° C. during the fixation step. In certain embodiments, thefixative is an aldehyde-based cross-linking fixative, such asglutaraldehyde- and/or formalin-based solutions. Examples of aldehydesfrequently used for immersion fixation include:

formaldehyde (standard working concentration of 5-10% formalin for mosttissues, although concentrations as high as 20% formalin have been usedfor certain tissues);

glyoxal (standard working concentration 17 to 86 mM);

glutaraldehyde (standard working concentration of 200 mM).

Aldehydes are often used in combination with one another. Standardaldehyde combinations include 10% formalin+1% (w/v) Glutaraldehyde.Atypical aldehydes have been used in certain specialized fixationapplications, including: fumaraldehyde, 12.5% hydroxyadipaldehyde (pH7.5), 10% crotonaldehyde (pH 7.4), 5% pyruvic aldehyde (pH 5.5), 10%acetaldehyde (pH 7.5), 10% acrolein (pH 7.6), and 5% methacrolein (pH7.6). Other specific examples of aldehyde-based fixative solutions usedfor immunohistochemistry are set forth in Table 1:

TABLE 1 Solution Standard Composition Neutral Buffered 5-20% formalin +phosphate buffer (pH ~6.8) Formalin Formal Calcium 10% formalin + 10 g/Lcalcium chloride Formal Saline 10% formalin + 9 g/L sodium chloride ZincFormalin 10% formalin + 1 g/L zinc sulphate Helly's Fixative 50 mL 100%formalin + 1 L aqueous solution containing 25 g/L potassium dichromate +10 g/L sodium sulfate + 50 g/L mercuric chloride B-5 Fixative 2 mL 100%formalin + 20 mL aqueous solution containing 6 g/L mercuric chloride +12.5 g/L sodium acetate (anhydrous) Hollande's Solution 100 mL 100%formalin + 15 mL Acetic acid + 1 L aqueous solution comprising 25 gcopper acetate and 40 g picric acid Bouin's Solution 250 mL 100%formalin + 750 mL saturated aqueous picric acid + 50 mL glacial aceticacid

In certain embodiments, the fixative solution is selected from Table 1.In some embodiments, the aldehyde concentration used is higher than theabove-mentioned standard concentrations. For example, ahigh-concentration aldehyde-based fixative solution can be used havingan aldehyde concentration that is at least 1.25-times higher than thestandard concentration used to fix a selected tissue forimmunohistochemistry with a substantially similar composition. In someexamples, the high-concentration aldehyde-based fixative solution isselected from: greater than 20% formalin, about 25% formalin or greater,about 27.5% formalin or greater, about 30% formalin or greater, fromabout 25% to about 50% formalin, from about 27.5% to about 50% formalin,from about 30% to about 50% formalin, from about 25% to about 40%formalin, from about 27.5% to about 40% formalin, and from about 30% toabout 40% formalin. As used in this context, the term “about” shallencompass concentrations that do not result in a statisticallysignificant difference in diffusion at 4° C. as measured by Bauer etal., Dynamic Subnanosecond Time-of-Flight Detection for Ultra-preciseDiffusion Monitoring and Optimization of Biomarker Preservation,Proceedings of SPIE, Vol. 9040, 90400B-1 (2014 Mar. 20).

Two-temperature fixation processes are especially useful for methods ofdetecting certain labile biomarkers in tissue samples, including, forexample, phosphorylated proteins, DNA, and RNA molecules (such as miRNAand mRNA). See PCT/EP2012/052800 (incorporated herein by reference).Thus, in certain embodiments, the fixed tissue samples obtained usingthese methods can be analyzed for the presence of such labile markers.Thus, in an embodiment, a method of detecting a labile marker is asample is provided, said method comprising fixing the tissue accordingto a two-temperature fixation as disclosed herein and contacting thefixed tissue sample with an analyte binding entity capable of bindingspecifically to the labile marker, such as FOXP3. Examples ofanalyte-binding entities include: antibodies and antibody fragments(including single chain antibodies), which bind to target antigens;t-cell receptors (including single chain receptors), which bind toMHC:antigen complexes; MHC: peptide multimers (which bind to specificT-cell receptors); aptamers, which bind to specific nucleic acid orpeptide targets; zinc fingers, which bind to specific nucleic acids,peptides, and other molecules; receptor complexes (including singlechain receptors and chimeric receptors), which bind to receptor ligands;receptor ligands, which bind to receptor complexes; and nucleic acidprobes, which hybridize to specific nucleic acids. For example, animmunohistochemical method of detecting a phosphorylated protein in atissue sample is provided, the method comprising contacting the fixedtissue obtained according to the foregoing two-temperature fixationmethod with an antibody specific for the phosphorylated protein anddetecting binding of the antibody to the phosphorylated protein. Inother embodiments, an in situ hybridization method of detecting anucleic acid molecule is provided, said method comprising contacting thefixed tissue obtained according to the foregoing two-temperaturefixation method with a nucleic acid probe specific for the nucleic acidof interest and detecting binding of the probe to the nucleic acid ofinterest.

The foregoing disclosure of the exemplary embodiments of the presentsubject disclosure has been presented for purposes of illustration anddescription. It is not intended to be exhaustive or to limit the subjectdisclosure to the precise forms disclosed. Many variations andmodifications of the embodiments described herein will be apparent toone of ordinary skill in the art in light of the above disclosure. Thescope of the subject disclosure is to be defined only by the claimsappended hereto, and by their equivalents.

Further, in describing representative embodiments of the present subjectdisclosure, the specification may have presented the method and/orprocess of the present subject disclosure as a particular sequence ofsteps. However, to the extent that the method or process does not relyon the particular order of steps set forth herein, the method or processshould not be limited to the particular sequence of steps described. Asone of ordinary skill in the art would appreciate, other sequences ofsteps may be possible. Therefore, the particular order of the steps setforth in the specification should not be construed as limitations on theclaims. In addition, the claims directed to the method and/or process ofthe present subject disclosure should not be limited to the performanceof their steps in the order written, and one skilled in the art canreadily appreciate that the sequences may be varied and still remainwithin the spirit and scope of the present subject disclosure.

1. A method for determining a reagent concentration comprising:immersing the sample in the reagent; obtaining an experimentaltime-of-flight versus time for the sample immersed in the reagent;providing a plurality of candidate diffusivity constants; simulating aspatial dependence of diffusion into the sample to generate a modeltime-of-flight versus time over a plurality of time points, wherein thesimulation is conducted for each of the candidate diffusivity constants;comparing the model time-of-flight versus time with the experimentaltime-of-flight versus time to obtain an error function, wherein aminimum of the error function yields a diffusivity constant for thesample; providing a plurality of candidate tissue porosities; simulatinga spatial dependence of diffusion into the sample to generate a modeltime-of-flight versus time over a plurality of time points, wherein thesimulation is conducted for each of the candidate porosities; comparingthe model time-of-flight with the experimental time-of-flight to obtaina second error function, wherein a minimum of the error function yieldsa porosity of the sample; and calculating a concentration of the reagentat one or more particular spatial points within the sample at aparticular time using the diffusivity constant for the sample and theporosity of the sample.
 2. The method of claim 1, wherein the simulatingof the spatial dependence of diffusion into the sample to generate themodel time-of-flight versus time over the plurality of time pointsutilizes the diffusivity constant for the sample.
 3. The method of claim1, wherein the calculating of the concentration of the reagent at theone or more particular spatial points with the sample at the particulartime comprises calculating a percent diffusion at the one or moreparticular spatial points at the particular time from the diffusivityconstant and time, and using the percent diffusion in the followingequation to yield the concentration:${reagent\_ conc} = {\left( {\% \mspace{14mu} {diffused}} \right)(\rho)\left( \frac{MWg\_ reagent}{1\mspace{14mu} {liter}} \right)\left( \frac{1\mspace{14mu} {mol}}{MWg\_ reagent} \right)}$4. The method of claim 1, wherein the reagent is selected from the groupconsisting of formaldehyde, ethanol, xylene, and paraffin.
 5. The methodof claim 4, wherein the molecular weight of paraffin is selected fromthe group consisting of a number average molecular weight (Mn), a weightaverage molecular weight (Mw), a viscosity average molecular weight(Mv), and combinations thereof.
 6. The method of claim 1, wherein thereagent comprises a formaldehyde solution and wherein the sample isremoved from the reagent once a concentration of the formaldehydesolution at a point at the center of the sample is at least above 90 mM.7. The method of claim 6, wherein the immersion of the sample in thereagent is performed as a cold step, and once the concentration at thepoint at the center of the sample is at least above 90 mM, thetemperature of the reagent is raised in a hot step.
 8. A method forfixing a tissue sample, comprising: immersing the tissue sample in acold formalin solution until a point at the center of the tissue sampleis determined to have a formaldehyde concentration of at least 90 mM,and contacting the tissue sample with a hot formalin solution onceformaldehyde concentration at the point at the center of the tissuesample is determined to be above 90 mM for a time sufficient to formcross-links, thereby fixing the tissue sample.
 9. The method of claim 8,wherein the immersing step is continued until a formaldehydeconcentration at the point at the center of the tissue sample isdetermined to have a formaldehyde concentration of at least 100 mM. 10.The method of claim 8, wherein the cold formalin solution has atemperature of less than about 20 degrees C. and the hot formalinsolution has a temperature of between about 20 degrees C. and about 55degrees C.
 11. The method of claim 8, wherein the contacting the tissuesample with the hot formalin solution comprises raising the temperatureof the cold formalin solution while the cold formalin solution remainsin contact with the tissue sample until it becomes a hot formalinsolution.
 12. The method of claim 8, wherein the formaldehydeconcentration is determined by a method selected from TOF, radio-labeltracing, mid-IR spectroscopy, and magnetic resonance.
 13. A system,comprising: an acoustic monitoring device that detects acoustic wavesthat have traveled through a tissue sample; one or more processorscommunicatively coupled to the acoustic monitoring device, wherein theone or more processors are configured to evaluate a speed of theacoustic waves based on a time-of-flight; one or more memoriescommunicatively coupled to the one or more processors, the one or morememories having stored thereon instructions, which when executed causethe processor to perform operations comprising: setting a range ofcandidate diffusivity constants for the tissue sample; simulating aspatial dependence of a reagent within the tissue sample for a pluralityof time points and for a first of candidate diffusivity points;determining a modeled time-of-flight based on the spatial dependence;repeating the spatial dependence simulation for each of the plurality ofdiffusivity constants; determining an error between themodeled-time-of-flight for the plurality of diffusivity constants versusan experimental time-of-flight for the tissue sample, wherein a minimumof an error function based on the error yields a diffusivity constantfor the tissue sample; setting a range of candidate porosities for thetissue sample that includes a plurality of candidate porosities;determining a second modeled time-of-flight based on the diffusivityconstant of the sample and a first of the plurality of candidateporosities, and determining a second error between the experimentaltime-of-flight and the second modeled time-of-flight; repeating thedetermination of the second modeled time-of-flight for others of theplurality of candidate porosities and their corresponding second errors,wherein a minimum of the error identifies the porosity of the sample;and calculating a spatial dependence of reagent concentration within thesample at a particular time from the identified diffusivity constant andthe identified porosity of the sample.
 14. The system of claim 13,wherein the memory further comprises instructions that when executedoutput a reagent concentration at the center of the sample at aparticular time.
 15. The system of claim 14, wherein the memory furthercomprises instructions that when executed terminate infusion of thesample with the reagent when the reagent concentration at the center ofthe tissue exceeds a pre-determined concentration threshold.
 16. Thesystem of claim 15, wherein the reagent comprises formaldehyde and thepredetermined concentration threshold is at least 90 mM.
 17. The systemof claim 15, wherein the system further comprises an alarm and thememory further includes instructions that when executed by the processorcause the alarm to sound once the reagent concentration at the center ofthe tissue exceeds the pre-determined threshold.
 18. The system of claim15, wherein the system further comprises a mechanism to remove thesample from the reagent and the memory further includes instructionsthat cause the mechanism to remove the sample from the reagent when thereagent concentration at the center of the tissue exceeds thepre-determined threshold.
 19. The system of claim 15, wherein thereagent comprises a cold formaldehyde solution having a temperature ofless than about 20 degrees C. and termination of the infusion comprisesraising the temperature of the formaldehyde solution to a temperature ofbetween about 20 degrees C. and about 55 degrees C. to provide a hotformaldehyde solution, wherein the system further includes a heater toheat the cold formaldehyde solution to a hot formaldehyde solution, andwherein memory further includes instructions that cause the heater toheat the cold formaldehyde solution to form the hot formaldehydesolution when the formaldehyde concentration at the center of the tissueexceeds about 90 mM.
 20. A tangible non-transitory computer-readablemedium having stored thereon instructions that cause a processor toperform operations comprising the steps of claim 1.